Solving by Completing the Square

Solving by Completing the Square

To solve an equation ax² + bx + c = 0 by completing the square:

a. If a ≠ 1 , multiply by $\frac{1}{a}$ so that the x²-coefficient is 1.

b. If the x²-coefficient is 1, add or subtract so that the equation is in the form

x² + bx = -c, or x² + $\frac{b}{a}$ x = – $\frac{c}{a}$ if step (a) has been applied.

c. Take half of the x-coefficient and square it. Add the result on both

sides of the equation.

d. Express the side with the variables as the square of a binomial.

e. Use the principle of square roots and complete the solution.