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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 .
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