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Lesson 10-3

Lesson 10-3. Solving Quadratic Equations by Completing the Square. Irrational Roots. Solve x 2 -10x + 25 = 7 by taking the square of each side. x 2 -10x + 25 = 7 Original Expression (x - 5) 2 = 7 Factored perfect square trinomial. Take the square root of both sides. Simplify.

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Lesson 10-3

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  1. Lesson 10-3 Solving Quadratic Equations by Completing the Square

  2. Irrational Roots Solve x2 -10x + 25 = 7 by taking the square of each side. x2 -10x + 25 = 7 Original Expression (x - 5)2 = 7Factored perfect square trinomial. Take the square root of both sides Simplify Add 5 to each side. Simplify

  3. Solve x2 + 6x +9 = 5 by talking the square root of each side. Round to the nearest tenth if necessary. {-5.2, -0.8}

  4. Key Concept To complete the square for a quadratic equation of the form x2 + bx, you can follow the steps below: Find 1/2 of b, the coefficient of x. Square the result of step 1 Addthe result of Step 2 to x2 + bx, the original expression.

  5. Complete the Square Find the value of c that makes x2 + 6x + c a perfect square. Find 1/2 of 6. 62 = 3 Square the result of step 1. 32 = 9 3. Addthe result of Step 2 to x2 + 6x, therefore x2 + 6x + 9. Factored, x2 + 6x + 9 = (x+3)2

  6. Find the value of c that makes x2 -12x +c a perfect square. 36

  7. Solve an Equation by Completing the Square Solve a2 -14a + 3 = -10 by completing the square. a2 -14a + 3 = -10Original Expression a2 -14a + 3-3 = -10-3Subtract 3 from each side. a2 - 14a = -13 Simplify. a2 - 14a + 49 = -13 + 49 Since (-14/2)2 = 49, add 49 to each side. (a - 7)2 = 36 Factor a2 - 14a + 49. a - 7 = 6 Take the square root of both sides. a - 7 + 7 = 6 + 7Add 7 to both sides. a = 7  6 Simplify. a = 7 + 6 or a = 7 - 6 a = 13 or a = 1

  8. Solve x2 -18x + 5 = -12 by completing the square. {1, 17}

  9. Solve -0.04x2 + 2x + 8 = 0 by completing the square. Solve a Quadratic Equation in Which a  1 -0.04x2 + 2x + 8 = 0Equation for where debris will land. Divide both sides by -0.04 x2 -50x -200 = 0 Simplify. x2 -50x -200 + 200 = 0 + 200Add 200 to both sides. x2 -50x = 200 Simplify. x2 -50x + 625= 200 + 625 Since (50/2)2 is 625, add 625 to both sides x2 -50x + 625= 825 Simplify. (x - 25)2 = 825 Factor x2 -50x + 625. Take square root of each side. Add 25 to each side Simplify or or

  10. Suppose the rate of flow of an 80-foot-wide river is given in the equation r = -0.01x2 + 0.8x, where r is the rate in miles per hour, and x is the distance from the shore in feet. Caden does not want to paddle his canoe against a current faster than 5 miles per hour. At what distance from the river bank must he paddle in order to avoid a current of 5 miles per hour? Within 7 feet of either bank

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