Basic Technical Mathematics, 11th Edition

7.2 Completing the Square

• Using the Square Root Property • Solving a Quadratic Equation by Completing the Square

Most quadratic equations that arise in applications cannot be solved by factoring. Therefore, we now develop a method called completing the square, which can be used to solve any quadratic equation. In the next section, this method is used to develop a general formula that can be used to solve any quadratic equation. Solving an equation by completing the square relies on the following property:

Square Root Property

If $x^2\hspace{0.17em}=\hspace{0.17em}k\hspace{0.17em},\hspace{0.17em}$ then $x\hspace{0.17em}=\hspace{0.17em}\hspace{0.17em}\pm \hspace{0.17em}\sqrt{k}\hspace{0.17em}.\hspace{0.17em}$

This property allows us to take the square root on both sides of an equation, but we must remember to include the positive and negative square root. There are actually two solutions,