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Expert-verified Found in: Page 315 ### Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465 # Solve $\text{}{x}^{2}-7x-30=0\text{.}$

The solution of the given equation is and $x=-3andx=10.$

See the step by step solution

## Step 1. Given information

The given equation is $\text{}{x}^{2}-7x-30=0\text{}$

We have to find the solution of the equation i.e the value of $x$ that satisfies the given equation.

## Step 2. Form the factors

$\begin{array}{l}\text{The given equation is}{x}^{2}-7x-30=0.\\ ⇒{x}^{2}-7x-30=0\\ ⇒{x}^{2}+3x-10x-30=0\text{}\left[\text{Split the middle term}\right]\\ ⇒x\left(x+3\right)-10\left(x+3\right)=0\text{}\left[\text{Take out the common terms}\right]\\ ⇒\left(x-10\right)\left(x+3\right)=0\text{}\left[\text{Form the factors}\right]\end{array}$

## Step 3. Solve for x

$\begin{array}{l}\text{By zero product rule,}\\ ⇒x-10=0\\ ⇒x=10\\ \text{and,}\\ ⇒x+3=0\\ ⇒x=-3\\ \text{The solution set is}\left\{-3,10\right\}\end{array}$ ### Want to see more solutions like these? 