Chapter 9, Problem 2QC

To determine

To find: The solution by using completing the square.

Answer to Problem 2QC

The solution of the equation $x^2+5x-6=0$ are $x=-\frac{3}{4}$ .

Explanation of Solution

Given information:

The given equation is $x^2+5x-6=0$ .

Calculation:

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

  $\begin{array}{c}{x}^2+5x-6=0\\ x^2+5x=6\end{array}$

Add ${\left[\frac{1}{2}\left(5\right)\right]}^2=\frac{25}{4}$ to both sides.

  $\begin{array}{c}{x}^2+5x+\frac{25}{4}=6+\frac{25}{4}\\ x^2+2\left(x\right)\left(\frac{5}{2}\right)+{\left(\frac{5}{2}\right)}^2=\frac{24+25}{4}\\ {\left(x+\frac{5}{2}\right)}^2=\frac{49}{4}\\ \left(x+\frac{5}{2}\right)=\frac{7}{4}\end{array}$

  $\begin{array}{c}x=\frac{7}{4}-\frac{5}{2}\\ x=-\frac{3}{4}\end{array}$

The solution of the equation $x^2+5x-6=0$ are $x=-\frac{3}{4}$ .

Therefore, the solution of the equation $x^2+5x-6=0$ are $x=-\frac{3}{4}$ .