Chapter 9, Problem 3QC

To determine

To find: The solution by using completing the square.

Answer to Problem 3QC

The solution of the equation $x^2-8x+15=0$ are $9\pm \sqrt{66}$ .

Explanation of Solution

Given information:

The given equation is $x^2-8x+15=0$ .

Calculation:

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

  $\begin{array}{c}{x}^2-8x+15=0\\ x^2-8x=-15\end{array}$

Add ${\left[\frac{1}{2}\left(-18\right)\right]}^2=81$ to both sides.

  $\begin{array}{c}{x}^2-8x+81=-15+81\\ x^2-2\left(x\right)\left(9\right)+{\left(9\right)}^2=66\\ {\left(x-9\right)}^2=66\\ \left(x-9\right)=\sqrt{66}\end{array}$

Using $\sqrt{a^2}=\left|a\right|$ .

  $\begin{array}{c}\left|x-9\right|=\sqrt{66}\\ x-9=\pm \sqrt{66}\\ x=9\pm \sqrt{66}\end{array}$

The solution of the equation $x^2-8x+15=0$ are $9\pm \sqrt{66}$ .

Therefore, the solution of the equation $x^2-8x+15=0$ are $9\pm \sqrt{66}$ .