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Lesson 58

Lesson 58. Completing the square. Factoring a perfect square trinomial. + 2ab + = ( a+b )( a+b )= = (a-b)(a-b) =. Square root property. The square root property can be used in solving quadratic equations in the form of a binomial square. If = a, where a>0, then x = or x = -

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Lesson 58

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  1. Lesson 58 Completing the square

  2. Factoring a perfect square trinomial • + 2ab + = ( a+b)(a+b)= • = (a-b)(a-b) =

  3. Square root property • The square root property can be used in solving quadratic equations in the form of a binomial square. • If = a, where a>0, then x = or x = - • So if = a, then x = +

  4. Solving equations that are perfect squares • Solve: - 10x + 25 = 9 • Factor (x-5)(x-5) = 9 • = 9 • Apply square root property • x-5 = + • x – 5 = + 3 • x = 5 + 3 • X = 5+3 =8 or x = 5-3 = 2

  5. practice • Solve: • + 6x + 9 = 64 • + 24x + 144 = 5 • - 14x + 49 = 10

  6. Completing the square • Some quadratic equations cannot be solved by factoring. • in these cases we can use completing the square • We can add a term to an expression to form a perfect square trinomial

  7. Completing the square • Given a quadratic of the form + bx, we can add to it the square of half the coefficient of x , , to create a perfect square trinomial • + bx + =

  8. Solve by completing the square • -14x -8 = 0 • +8 +8 move constant term • - 14x = 8 take half of the coefficient of x and square it and add it to both sides • - 14x + = 8 + • = 8 + • = 8 + 49 • = 57 • x-7 = + x = 7 +

  9. Steps for completing the square • Step 1 Divide all terms by a (the coefficient of x2). • Step 2 Move the number term (c/a) to the right side of the equation. • Step 3 Complete the square on the left side of the equation and balance this by adding the same value to the right side of the equation. • Step 4 Take the square root on both sides of the equation. • Step 5 Add or subtract the number that remains on the left side of the equation to find x.

  10. practice • Solve by completing the square. • -10x + 19 = 0 • -5x – 18 = 0 • + 10x + 18 = 0 • 2 - 5x – 18 = 0

  11. Example 4 p. 416

  12. Question 1 • What number should be added to x2 – (3/2)x to complete the square? • [ Edit ] • (No guessing! Be sure of your answer.) • A • -9/16 • B • 9/16 • C • -3/4 • D • 3/4

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