Solving Quadratic Equations by Completing the Square

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Solving Quadratic Equations by Completing the Square

Example

Completing the square with a ≠ 1

Solve 2x² + 3x - 2 = 0 by completing the square.

Solution

For completing the square, the coefficient of x² must be 1. So we first divide each side of the equation by 2:

				Divide each side by 2.
			= 0	Simplify.
			= 1	Get only x² and x terms on the left-hand side.

				Factor the left-hand side
				Even-root property
	or
x	or	x

Check these values in the original equation. The solution set is