Chapter 12.5, Problem 7WE

To determine

Solve the quadratic equation.

Answer to Problem 7WE

  $x=-3\pm \sqrt{14}$

Explanation of Solution

Given:

The equation is :

  $x^2+6x=5$

Calculation:

The given equation $x^2+6x=5\Rightarrow x^2+6x-5=0$ is of the type $x^2+bx+c=0$ , where b = 6 , which is even .

So, it can be solved by Completing the square.

So,

  $\begin{array}{l}{x}^2+6x=5\\ \Rightarrow x^2+6x+9=5+\mathrm{9...........}[\text{add }{\left(\frac{6}{2}\right)}^3\text{ each side]}\\ \Rightarrow {\left(x+3\right)}^2=14\\ \Rightarrow x+3=\pm \sqrt{14}\mathrm{................}[\text{take square root each side]}\\ \Rightarrow x=-3\pm \sqrt{14}\mathrm{................}[\text{subtract 3 from each side]}\end{array}$