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## Solving Quadratic Equations – Word problems

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**Solving Quadratic Equations – Word problems**When solving word problems, it is important to look for key words such as product, total, sum, difference, quotient, area, perimeter, etc to help you set up your equations. We will use either factoring or the quadratic formula to find our solutions. Read the problem carefully and set up your equations.**Solving Quadratic Equations – Word problems**When solving word problems, it is important to look for key words such as product, total, sum, difference, quotient, area, perimeter, etc to help you set up your equations. We will use either factoring or the quadratic formula to find our solutions. Read the problem carefully and set up your equations. EXAMPLE # 1 : Two consecutive positive numbers have a product of 42. Find the two numbers. Let the first number = x**Solving Quadratic Equations – Word problems**When solving word problems, it is important to look for key words such as product, total, sum, difference, quotient, area, perimeter, etc to help you set up your equations. We will use either factoring or the quadratic formula to find our solutions. Read the problem carefully and set up your equations. EXAMPLE # 1 : Two consecutive positive numbers have a product of 42. Find the two numbers. Let the first number = x Let the second number = x + 1 Consecutive integers are next to each other. So the next integer would be 1 greater.**Solving Quadratic Equations – Word problems**When solving word problems, it is important to look for key words such as product, total, sum, difference, quotient, area, perimeter, etc to help you set up your equations. We will use either factoring or the quadratic formula to find our solutions. Read the problem carefully and set up your equations. EXAMPLE # 1 : Two consecutive positive numbers have a productof 42 . Find the two numbers. Let the first number = x Let the second number = x + 1 Product means multiply…**Solving Quadratic Equations – Word problems**When solving word problems, it is important to look for key words such as product, total, sum, difference, quotient, area, perimeter, etc to help you set up your equations. We will use either factoring or the quadratic formula to find our solutions. Read the problem carefully and set up your equations. EXAMPLE # 1 : Two consecutive positive numbers have a productof 42 Find the two numbers. Let the first number = x Let the second number = x + 1 Distribute…**Solving Quadratic Equations – Word problems**When solving word problems, it is important to look for key words such as product, total, sum, difference, quotient, area, perimeter, etc to help you set up your equations. We will use either factoring or the quadratic formula to find our solutions. Read the problem carefully and set up your equations. EXAMPLE # 1 : Two consecutive positive numbers have a productof 42. Find the two numbers. Let the first number = x Let the second number = x + 1 Get 42 on the other side so we have our equation = zero…**Solving Quadratic Equations – Word problems**When solving word problems, it is important to look for key words such as product, total, sum, difference, quotient, area, perimeter, etc to help you set up your equations. We will use either factoring or the quadratic formula to find our solutions. Read the problem carefully and set up your equations. EXAMPLE # 1 : Two consecutive positive numbers have a productof 42. Find the two numbers. Let the first number = x Let the second number = x + 1 FACTOR…**Solving Quadratic Equations – Word problems**When solving word problems, it is important to look for key words such as product, total, sum, difference, quotient, area, perimeter, etc to help you set up your equations. We will use either factoring or the quadratic formula to find our solutions. Read the problem carefully and set up your equations. EXAMPLE # 1 : Two consecutive positive numbers have a productof 42. Find the two numbers. Let the first number = x Let the second number = x + 1 We are looking for a positive pair so let x = 6 and ( x + 1 ) = 7**Solving Quadratic Equations – Word problems**When solving word problems, it is important to look for key words such as product, total, sum, difference, quotient, area, perimeter, etc to help you set up your equations. We will use either factoring or the quadratic formula to find our solutions. Read the problem carefully and set up your equations. EXAMPLE # 1 : Two consecutive positive numbers have a productof 42. Find the two numbers. Let the first number = x Let the second number = x + 1 (6)(7) = 42 so the solution set is We are looking for a positive pair so let x = 6 and ( x + 1 ) = 7**Solving Quadratic Equations – Word problems**When solving word problems, it is important to look for key words such as product, total, sum, difference, quotient, area, perimeter, etc to help you set up your equations. We will use either factoring or the quadratic formula to find our solutions. Read the problem carefully and set up your equations. EXAMPLE # 2 : Two consecutive positive even numbers have a product of 24. Find the two numbers.**Solving Quadratic Equations – Word problems**When solving word problems, it is important to look for key words such as product, total, sum, difference, quotient, area, perimeter, etc to help you set up your equations. We will use either factoring or the quadratic formula to find our solutions. Read the problem carefully and set up your equations. EXAMPLE # 2 : Two consecutive positive even numbers have a product of 24. Find the two numbers. Let the first number = x**Solving Quadratic Equations – Word problems**When solving word problems, it is important to look for key words such as product, total, sum, difference, quotient, area, perimeter, etc to help you set up your equations. We will use either factoring or the quadratic formula to find our solutions. Read the problem carefully and set up your equations. EXAMPLE # 2 : Two consecutive positive even numbers have a product of 24. Find the two numbers. Let the first number = x Let the second number = x + 2 Consecutive even integers, so the next integer would be 2 greater.**Solving Quadratic Equations – Word problems**When solving word problems, it is important to look for key words such as product, total, sum, difference, quotient, area, perimeter, etc to help you set up your equations. We will use either factoring or the quadratic formula to find our solutions. Read the problem carefully and set up your equations. EXAMPLE # 2 : Two consecutive positive even numbers have a product of 24. Find the two numbers. Let the first number = x Let the second number = x + 2 Product implies multiplication…**Solving Quadratic Equations – Word problems**When solving word problems, it is important to look for key words such as product, total, sum, difference, quotient, area, perimeter, etc to help you set up your equations. We will use either factoring or the quadratic formula to find our solutions. Read the problem carefully and set up your equations. EXAMPLE # 2 : Two consecutive positive even numbers have a product of 24. Find the two numbers. Let the first number = x Let the second number = x + 2 Distribute and get 24 on the other side…**Solving Quadratic Equations – Word problems**When solving word problems, it is important to look for key words such as product, total, sum, difference, quotient, area, perimeter, etc to help you set up your equations. We will use either factoring or the quadratic formula to find our solutions. Read the problem carefully and set up your equations. EXAMPLE # 2 : Two consecutive positive even numbers have a product of 24. Find the two numbers. Let the first number = x Let the second number = x + 2 Factor…**Solving Quadratic Equations – Word problems**When solving word problems, it is important to look for key words such as product, total, sum, difference, quotient, area, perimeter, etc to help you set up your equations. We will use either factoring or the quadratic formula to find our solutions. Read the problem carefully and set up your equations. EXAMPLE # 2 : Two consecutive positive even numbers have a product of 24. Find the two numbers. Let the first number = x Let the second number = x + 2 We are looking for positive numbers so let x = 4 and x + 2 = 6**Solving Quadratic Equations – Word problems**When solving word problems, it is important to look for key words such as product, total, sum, difference, quotient, area, perimeter, etc to help you set up your equations. We will use either factoring or the quadratic formula to find our solutions. Read the problem carefully and set up your equations. EXAMPLE # 2 : Two consecutive positive even numbers have a product of 24. Find the two numbers. Let the first number = x Let the second number = x + 2 (4)(6) = 24 so solution set is We are looking for positive numbers so let x = 4 and x + 2 = 6**Solving Quadratic Equations – Word problems**Another type of problem involves area of a rectangle. Area of a rectangle is defined as length times width.**Solving Quadratic Equations – Word problems**Another type of problem involves area of a rectangle. Area of a rectangle is defined as length times width. Width Length**Solving Quadratic Equations – Word problems**Another type of problem involves area of a rectangle. Area of a rectangle is defined as length times width. Width Length So if L = 4 and W = 6, you would have an area of 24 square units.**Solving Quadratic Equations – Word problems**Another type of problem involves area of a rectangle. Area of a rectangle is defined as length times width. Width Length So if L = 4 and W = 6, you would have an area of 24 square units. Let’s take a look at a word problem involving area of a rectangle.**Solving Quadratic Equations – Word problems**EXAMPLE # 3 : Find the length and width of a rectangle whose length is 5 feet longer than its width with an area of 36 square feet.**Solving Quadratic Equations – Word problems**EXAMPLE # 3 : Find the length and width of a rectangle whose length is 5 feet longer than its width with an area of 36 square feet. Let W be the width… W**Solving Quadratic Equations – Word problems**EXAMPLE # 3 : Find the length and width of a rectangle whose length is 5 feetlonger than its width with an area of 36 square feet. W + 5 Let W be the width… So L = W + 5 W**Solving Quadratic Equations – Word problems**EXAMPLE # 3 : Find the length and width of a rectangle whose length is 5 feet longer than its width with an area of 36 square feet. W + 5 Let W be the width… So L = W + 5 W**Solving Quadratic Equations – Word problems**EXAMPLE # 3 : Find the length and width of a rectangle whose length is 5 feet longer than its width with an area of 36 square feet. W + 5 Let W be the width… So L = W + 5 W**Solving Quadratic Equations – Word problems**EXAMPLE # 3 : Find the length and width of a rectangle whose length is 5 feet longer than its width with an area of 36 square feet. 9 feet Let W be the width… So L = W + 5 4 feet Throw out the negative answer and you get W = 4 feet L = W + 5 = 9 feet