Algebra 12.4 Completing the Square

Solve: x² + 10x - 24 = 0 (x + 12)(x - 2) = 0 -12, 2 -12, 2 The 3 Methods of Solving a Quadratic Equation in the form ax²+ bx + c = 0 Solve: x² + 10x - 24 = 0 1. Factoring (x + 12)(x - 2) = 0 -12, 2 2. Quadratic Formula -12, 2 3. Completing the Square We learn today

Solve x² + 10x - 24 = 0 by Completing the Square Move constant to right and leave a space x² + 10x = 24 +25 +25 Take ½ of b and square it. Add result to both sides. (x + 5 )² = 49 Simplify both sides (left side is a PST) x + 5 = ± √49 Take square root of both sides x = -5 ± 7 Isolate x to solve -12, 2

STEPS Completing the Square: 1.Write equation as ax²+ bx (space) = c 2. Add to both sides 3. Write left side as PST and simplify right side 4. Take the square root of both sides 5. Isolate x to solve

Warm-Up: What would you add to “complete the square?” Expression 10 100 x²+ 20x 16 -4 x²- 8x x²+ 5x Take ½ the numerator Double the denominator

Try it together: x²- 8x + 12 = 0 Move constant to right and leave a space x² - 8x = -12 +16 +16 Take ½ of b and square it. Add result to both sides. (x - 4 )² = 4 Simplify both sides (left side is a PST) x - 4 = ± √4 Take square root of both sides x = 4 ± 2 Isolate x to solve 6, 2

Try it together: x²- 6x - 11 = 0 Move constant to right and leave a space x² - 6x = 11 + 9 +9 Take ½ of b and square it. Add result to both sides. (x - 3 )² = 20 Simplify both sides (left side is a PST) x – 3 = ± √20 Take square root of both sides x = 3 ± 2√5 Isolate x to solve

Try it together: x²- 2/3x - 3 = 0 Move constant to right and leave a space x² - 2/3x = 3 +1/9 +1/9 Take ½ of b and square it. Add result to both sides. (x - 1/3 )² = 28/9 Simplify both sides (left side is a PST) x – 1/3 = ± Take square root of both sides x = ± Isolate x to solve Simplify over one denominator

Homework pg. 734 # 3-37 odd Skip #13 and 15 Let’s Look at #17