Chapter 4.6, Problem 38PPS

To determine

The value of the variable.

Answer to Problem 38PPS

  $x=-8,3$

Explanation of Solution

Given:

The given figure is:

  

Calculation:

Angles opposite to equal sides will be equal. The sum of angles of a triangle is equal.

The value of x will be:

  $\begin{array}{l}{x}^2+5x=24\\ x^2+5x-24=0\\ x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\ x=\frac{-5\pm \sqrt{5^2-4\left(1\right)\left(-24\right)}}{2\left(1\right)}\\ x=\frac{-5\pm 11}{2}\\ x=-8,3\end{array}$