### Select your language

Suggested languages for you:

Americas

Europe

Q23.

Expert-verified
Found in: Page 492

### Algebra 1

Book edition Student Edition
Author(s) Carter, Cuevas, Day, Holiday, Luchin
Pages 801 pages
ISBN 9780078884801

### Answers without the blur.

Just sign up for free and you're in.

# Solve each equation. Check your solutions.${x}^{2}-5x=14$

The solution of ${x}^{2}-5x=14$ is role="math" localid="1647953707701" $\mathbit{x}\mathbf{=}\mathbf{7}\mathbf{,}\mathbf{-}\mathbf{2}$.

See the step by step solution

## Step 1. Subtract.

Subtract from both sides of the given equation.

${x}^{2}-5x-14=14-14\phantom{\rule{0ex}{0ex}}=0$

## Step 2. Factor by using GCF.

Factor by using GCF to get the form $xy=0$.

$\left(x-7\right)\left(x+2\right)=0$

## Step 3. Write zero product property.

For any real numbers $x$ and $y$, if $xy=0$ then $x=0,y=0$ or both $x$ and $y$ equal to zero.

## Step 4. Apply zero product property.

Apply zero product property to the given equation, $\left(x-7\right)\left(x+2\right)=0$.

localid="1647954254435" $x-7=0\text{or}x+2=0\phantom{\rule{0ex}{0ex}}\text{}x=7\text{}x=-2$

Therefore, the roots are 7 and $-2$.

## Step 5. Check the obtained solution.

To check whether the obtained solution is correct or not, substitute 7 for $x$ and $-2$ for $x$ in the given equation and simplify.

role="math" localid="1647954142827" ${\left(7\right)}^{2}-5\left(7\right)\stackrel{?}{=}14\phantom{\rule{0ex}{0ex}}49-35\stackrel{?}{=}14\phantom{\rule{0ex}{0ex}}14=14\phantom{\rule{0ex}{0ex}}LHS=RHS$

${\left(-2\right)}^{2}-5\left(-2\right)\stackrel{?}{=}14\phantom{\rule{0ex}{0ex}}4+10\stackrel{?}{=}14\phantom{\rule{0ex}{0ex}}14=14\phantom{\rule{0ex}{0ex}}LHS=RHS$

Therefore, the obtained solution is correct.

### Want to see more solutions like these?

Sign up for free to discover our expert answers

## Recommended explanations on Math Textbooks

94% of StudySmarter users get better grades.