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Solving the Quadratic Equation by Completing the Square

10.7. Solving the Quadratic Equation by Completing the Square. How would you factor x 2 -6x+7=0?. Complete the square when the leading coefficient is 1. Steps to “Completing the Square”. Subtract “c” from both sides of the equal sign. Find ( 1 / 2 b) 2

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Solving the Quadratic Equation by Completing the Square

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  1. 10.7 Solving the Quadratic Equation by Completing the Square

  2. How would you factor x2-6x+7=0? Complete the square when the leading coefficient is 1.

  3. Steps to “Completing the Square” • Subtract “c” from both sides of the equal sign. • Find (1/2b)2 • Add that value to both sides of the equal sign. • Factor the perfect square trinomial. • Tip: Substitute the value of “1/2b” into the parentheses to make a perfect square trinomial.(x + ___)2 = {c + (1/2b)2} • Take the square root of both sides. • Solve for x.

  4. Practice the steps to completing the square. x2-6x+7=0 X2 - 6x =-7 Subtract 7 Add (½ b)2 to each side. (1/2(-6))2 = 9 x2-6x+9=-7+9 Make perfect square trinomial

  5. Tip: Put ½ b into the ( ) with sign from original. (x-3)2=2 Take sq. root Add 3 to both sides Two Answers

  6. x2+5x-8=0 PRACTICE • x2 + 5x = 8 • (1/2∙5)2 = 25/4 = 6¼ • x2 + 5x + 25/4 = 8 + 6¼ • x2 + 5x + 25/4 = 14¼ • (x + 5/2)2 = 14¼ • x = ± √14 ¼ - 5/2

  7. Practice: x2-4x+2=0 • x2 - 4x = -2 • (1/2 (-4))2 = 4 • x2 - 4x + 4 = -2 + 4 • x2 - 4x + 4 = 2 • (x - 2)2 = 2 • x = ± √2 + 2

  8. Solve when the coefficient isn’t 1! 4x2-4x-15=0 Original: divide each term by 4 to get x2 alone.

  9. (x- )2 = 4 x =  2 +

  10. What method is best?

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