Chapter 4.6, Problem 1AGP

To determine

The solutions using quadratic formula.

Answer to Problem 1AGP

The solutions are $2,-8$ .

Explanation of Solution

Given:

  $\begin{array}{l}{x}^2+6x=16\\ x^2+6x-16=0\end{array}$

Calculation:

Quadratic formula equation,

  $\begin{array}{l}a{x}^2+bx+c=0,\\ x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\end{array}$

Now,

  $x^2+6x-16=0$

  $\begin{array}{l}x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\ =\frac{-\left(6\right)\pm \sqrt{{\left(6\right)}^2-4\left(1\right)\left(-16\right)}}{2\left(1\right)}\\ =\frac{-6\pm 10}{2}\\ x=\frac{-6+10}{2}\text{or}x=\frac{-6-10}{2}\\ x=2,-8\end{array}$

Therefore,

The solutions are $2,-8$ .