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Name______________________________________ Solving Quadratic Equations by Completing the Square Steps: ax2 + bx + c = 0 Given: 2x2 = -8x + 12 1. Collect variable terms on 1 side and constants on the other side. 2x2 + 8x = 12 2. If needed, divide both sides by a to make the 2(x2 + 4x ____) = 12 ____ 2 coefficient of the x term 1. 2(x2 + 4x + 4) = 12 + 4(2) 2 3. Complete the square by adding (b/2) to both 2(x2 + 4x + 4) = 20 sides of the equation. 2(x + 2)2 = 20 4. Factor the variable expression as a perfect square. (x + 2)2 = 10 5. Take the square root of both sides of the equation. x + 2 = ±√10 6. Solve for the values of the variable. x = -2 ±√10 __________________________________________________________________________________________________ Solve : 1. x2 + 8 = 6x 2. 4x + x2 = 24 3. x2 – 4x = -1 4. 2x2 + 8x - 16= 0 5. 4x2 + 11 = 59 6. (x+10)2 = 6 Name______________________________________ Solving Quadratic Equations by Completing the Square Steps: ax2 + bx + c = 0 Given: 2x2 = -8x + 12 1. Collect variable terms on 1 side and constants on the other side. 2x2 + 8x = 12 2 2. If needed, divide both sides by a to make the 2(x + 4x ____) = 12 ____ 2 coefficient of the x term 1. 2(x2 + 4x + 4) = 12 + 4(2) 3. Complete the square by adding (b/2)2 to both 2(x2 + 4x + 4) = 20 sides of the equation. 2(x + 2)2 = 20 4. Factor the variable expression as a perfect square. (x + 2)2 = 10 5. Take the square root of both sides of the equation. x + 2 = ±√10 6. Solve for the values of the variable. x = -2 ±√10 __________________________________________________________________________________________________ Solve : 1. x2 + 8 = 6x 2. 4x + x2 = 24 3. x2 – 4x = -1 4. 2x2 + 8x - 16= 0 5. 4x2 + 11 = 59 6. (x+10)2 = 6