Chapter 4.9, Problem 1ST

To determine

To solve:The given equation.

Answer to Problem 1ST

The simplified answer is $\left[x=14,-3\right]$

Explanation of Solution

Given information:

The term is given as: $x^2-11x-42=0$

Formula used:use factor formula.

Calculation:

The given equation can be solved as:

  $\begin{array}{l}{x}^2-11x-42=0\\ x=\frac{-b\pm \sqrt{{\left(b\right)}^2-4ac}}{2a}\text{ use factor formula}\text{.}\\ x=\frac{-\left(-11\right)\pm \sqrt{{\left(-11\right)}^2-4\times 1\times \left(-42\right)}}{2}\\ x=\frac{11\pm \sqrt{121+168}}{2}\\ x=\frac{11\pm 17}{2}\\ \text{Either}\\ x=\frac{11+17}{2}\\ x=14\\ \text{or}\\ x=\frac{11-17}{2}\\ x=-3\\ \text{Hence }\left[x=14,-3\right]\text{.}\end{array}$