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## Solving Quadratic Equations by Completing the Square

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**Solving Quadratic Equations by Completing the Square**Solve the following equation by completing the square: Step 1: Isolate the constant**Solving Quadratic Equations by Completing the Square**Step 2: Find the term that completes the square on the left side of the equation. It is half the coefficient of the linear term squared. Add that term to both sides.**Solving Quadratic Equations by Completing the Square**Step 3: Factor the perfect square trinomial on the left side of the equation. Simplify the right side of the equation.**Solving Quadratic Equations by Completing the Square**Step 4: Take the square root of each side**Solving Quadratic Equations by Completing the Square**Step 5: Set up the two possibilities and solve**Let's solve another one by completing the square.**25 25 Since it doesn't factor get the constant on the other side ready to complete the square. So what do we add to both sides? the middle term's coefficient divided by 2 and squared Factor the left hand side Square root both sides (remember ) Subtract 5 from both sides to get x alone**Let's solve another one by completing the square.**To complete the square we want the coefficient of the x2 term to be 1. 2 2 2 2 Divide everything by 2 16 16 Since it doesn't factor get the constant on the other side ready to complete the square. So what do we add to both sides? the middle term's coefficient divided by 2 and squared Factor the left hand side Square root both sides (remember ) Add 4 to both sides to get x alone**You try:**• x2 - 8x + 3 = 0 • x2 -10x +7 = 0 • 5x2 – 20x -71 = -6 • 2x2 – 8x – 29 = -9