Chapter 9, Problem 1QC

To determine

To find: The solution by using completing the square.

Answer to Problem 1QC

The solution of the equation $x^2+8x+7=0$ are $x=-1$ .

Explanation of Solution

Given information:

The givenequation is $x^2+8x+7=0$ .

Calculation:

Isolate the variable on one side and the constant terms on the other.

  $\begin{array}{c}{x}^2+8x+7=0\\ x^2+8x=-7\end{array}$

Add ${\left[\frac{1}{2}\left(8\right)\right]}^2=16$ to both sides.

  $\begin{array}{c}{x}^2+8x+16=-7+16\\ x^2+2\left(x\right)\left(4\right)+{\left(4\right)}^2=9\\ {\left(x+4\right)}^2=9\\ \left(x+4\right)=3\end{array}$

  $x=-1$

The solution of the equation $x^2+8x+7=0$ are $x=-1$ .

Therefore ,the solution of the equation $x^2+8x+7=0$ are $x=-1$ .