Chapter 8: Q23. (page 492)

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

Short Answer

Expert verified

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

Step by step solution

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.

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

Short Answer

Step by step solution

Step 1. Subtract.

Step 2. Factor by using GCF.

Step 3. Write zero product property.

Step 4. Apply zero product property.

Step 5. Check the obtained solution.

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Solve each equation. Check your solutions.x2-5x=14

Short Answer

Step by step solution

Step 1. Subtract.

Step 2. Factor by using GCF.

Step 3. Write zero product property.

Step 4. Apply zero product property.

Step 5. Check the obtained solution.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Theoretical and Mathematical Physics

Calculus

Statistics

Pure Maths

Mechanics Maths

Study anywhere. Anytime. Across all devices.

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