Completing the Square

Method for x2 + bx + c = 0

1. Take half the coefficient of x, square it.
2. x2 + bx = (x + b/2)2 - (b/2)2

Example: Solve x2 + 6x + 5 = 0

x2 + 6x = -5
(x + 3)2 - 9 = -5
(x + 3)2 = 4
x + 3 = ±2
x = -1 or x = -5

If a ≠ 1

Divide through by a first.

Example: 2x2 - 8x + 6 = 0   ⇒   x2 - 4x + 3 = 0
(x - 2)2 - 4 + 3 = 0   ⇒   (x - 2)2 = 1   ⇒   x = 1 or 3

Use: This method works for all quadratics and is used to derive the formula.

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Related Exercises

Solve by completing the square

Solve by completing the square. Leave surds in your answer if needed:x2 + 4x - 5 = 0x2 - 6x …

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