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Q23.

Expert-verified

Algebra 1

Found in: Page 492

Book edition Student Edition

Author(s) Carter, Cuevas, Day, Holiday, Luchin

Pages 801 pages

ISBN 9780078884801

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Short Answer

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

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

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Subtract.

Subtract from both sides of the given equation.

$x^{2} - 5 x - 14 = 14 - 14 = 0$

Step 2. Factor by using GCF.

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

$(x - 7) (x + 2) = 0$

Step 3. Write zero product property.

For any real numbers $x$ and $y$ , if $x y = 0$ 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, $(x - 7) (x + 2) = 0$ .

localid="1647954254435" $x - 7 = 0 or x + 2 = 0 x = 7 x = - 2$

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" ${(7)}^{2} - 5 (7) \overset{?}{=} 14 49 - 35 \overset{?}{=} 14 14 = 14 L H S = R H S$

${(- 2)}^{2} - 5 (- 2) \overset{?}{=} 14 4 + 10 \overset{?}{=} 14 14 = 14 L H S = R H S$

Therefore, the obtained solution is correct.

Most popular questions for Math Textbooks

Find the greatest common factor of each set of monomials.

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$x^{2} - 4 x - 21$

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