Chapter 9.5, Problem 1LC

To determine

The solution of each equation by completing the square.

Answer to Problem 1LC

The solution of the given equation is $x=10,-18$ .

Explanation of Solution

Given:

The given equation is:

  $x^2+8x=180$

Calculation:

Calculate the values for x:

  $\begin{array}{l}{x}^2+8x=180\\ \text{Add }{\left(\frac{8}{2}\right)}^2={\left(4\right)}^2\text{ to both sides:}\\ x^2+8x+{\left(4\right)}^2=180+{\left(4\right)}^2\\ {\left(x+4\right)}^2=180+16\\ {\left(x+4\right)}^2=196\\ x+4=\pm \sqrt{196}\\ x+4=\pm 14\\ x+4=14\text{ or }x+4=-14\\ x=10\text{ or }x=-18\\ x=10,-18\end{array}$

The solution of the given equation is $x=10,-18$ .