Algebra

Completing the Square

Introduction

To find the solution set of a quadratic equation \(ax^2 + bx + c = 0\) \((a \neq 0)\) is by the method of completing the square. It is done as follows:

1. Check if \(a = 1\). If \(a = 1\) proceed to step 2. If \(a \neq 1\), we divide both sides by \(a\).
2. Rewrite the equation so that both terms containing variables are on one side of the equals sign, and the constant is on the other side.
3. Take half the coefficient of \(x\) and square it.
4. Add the squared value to both sides.
5. One side should now be a perfect square trinomial, from which the equation can be solved. Factor the trinomial.
6. Take the square root of both sides.
7. Solve for \(x\).