Chapter 12.4, Problem 4ST

To determine

To solve: the given equation for $x$ by completing square method.

Answer to Problem 4ST

  $x=8,-2$

Explanation of Solution

Given:

Given equation

  $x^2-6x-16=0$

Concept used:

A perfect square trinomial is of the form $a^2+2ab+b^2$ and the perfect square will be

  $a^2+2ab+b^2={\left(a+b\right)}^2$

Calculation:

Consider the given equation,

  $x^2-6x-16=0$

Make the left side a perfect square of the above equation by completing square method as shown:

  $\begin{array}{c}{x}^2-6x+9=16+9\\ x^2-2\cdot x\cdot 3+3^2=25\\ {\left(x-3\right)}^2=5^2\end{array}$

The equation can be solved by square root as:

  $\begin{array}{c}{\left(x-3\right)}^2=5^2\\ x-3=\pm \sqrt{5^2}\\ x=\pm 5+3\\ x=8,-2\end{array}$

Hence, the solution is $x=8,-2$ .