16.4 solving quadratics by completing the square
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This document discusses solving quadratic equations by completing the square. It provides examples of perfect square trinomials like x^2 + 6x + 9 and shows how to find the missing constant term when it is not present. The steps for completing the square to solve an equation are outlined: 1) move all terms to the left side, 2) add the completing the square term to both sides, 3) factor the perfect square trinomial, 4) take the square root of both sides, and 5) solve the resulting equations for x.
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16.4 solving quadratics by completing the square
- 1. Solving Quadratic Equations by Completing the Square 16.4
- 2. Perfect Square Trinomials Examples x2 + 6x + 9 x2 - 10x + 25 x2 + 12x + 36
- 3. Creating a Perfect Square Trinomial In the following perfect square trinomial, the constant term is missing. X2 + 14x + ____ Find the constant term by squaring half the coefficient of the linear term. (14/2)2 X2 + 14x + 49
- 4. Perfect Square Trinomials Create perfect square trinomials. x2 + 20x + ___ x2 - 4x + ___ x2 + 5x + ___ 100 4 25/4
- 5. Solving Quadratic Equations by Completing the Square Solve the following equation by completing the square: Step 1: Move quadratic term, and linear term to left side of the equation 2 8 20 0x x+ − = 2 8 20x x+ =
- 6. Solving Quadratic Equations by Completing the Square Step 2: Find the term that completes the square on the left side of the equation. Add that term to both sides. 2 8 =20 +x x+ + W W 2 8 2016 16x x+ + = + **REMEMBER: (b/2)2 ** (8/2)2 = (4) 2 = 16
- 7. 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. 2 8 2016 16x x+ + = + (x + 4)(x + 4) = 36 (x + 4)2 = 36
- 8. Solving Quadratic Equations by Completing the Square Step 4: Take the square root of each side 2 ( 4) 36x + = ( 4) 6x + = ± Step 5: Set up the two possibilities and solve 4 6 4 6 and 4 6 10 and 2x= x x x x = − ± = = − − − = − +