Chapter 9: Q. 9.7 (page 863)

Solve $\frac{1}{2} x^{2} + 4 = 24$

Short Answer

Expert verified

The solutions of the quadratic equation: $x = 2 \sqrt{10}, x = - 2 \sqrt{10}$

Step by step solution

Step 1. Given information

Consider the quadratic equation

$\frac{1}{2} x^{2} + 4 = 24$

The objective is to solve the quadratic equation by using square root property.

If $x^{2} = k$ , then $x = \pm \sqrt{k}$

Isolate the quadratic term.

$\frac{1}{2} x^{2} = 24 - 4 \frac{1}{2} x^{2} = 20$

Multiply by $\frac{2}{1}$ to make the coefficient 1.

$\frac{2}{1} \cdot \frac{1}{2} x^{2} = \frac{2}{1} \cdot 20 x^{2} = 40$

Use the Square Root Property.

$x = \pm \sqrt{40}$

Step 2. Simplify the expression.

Simplify the radical.

$x = \pm \sqrt{10 \cdot 4} x = \pm 2 \sqrt{10}$

Rewrite to show two solutions.

$x = 2 \sqrt{10}, x = - 2 \sqrt{10}$

Step 3. Check the solutions:

Substitute $x = 2 \sqrt{10}$ in the original solution.

role="math" localid="1645359951214" $\frac{1}{2} x^{2} + 4 = 24 \frac{1}{2} {(2 \sqrt{10})}^{2} + 4 \overset{?}{=} 24 \frac{1}{2} (40) + 4 \overset{?}{=} 24 24 = 24$

Substitute $x = - 2 \sqrt{10}$ in the original solution.

$\frac{1}{2} x^{2} + 4 = 24 \frac{1}{2} {(- 2 \sqrt{10})}^{2} + 4 \overset{?}{=} 24 \frac{1}{2} (40) + 4 \overset{?}{=} 24 24 = 24$

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Solve $\frac{1}{2} x^{2} + 4 = 24$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Simplify the expression.

Step 3. Check the solutions:

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Solve12x2+4=24

Short Answer

Step by step solution

Step 1. Given information

Step 2. Simplify the expression.

Step 3. Check the solutions:

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

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Applied Mathematics

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Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Solve $\frac{1}{2} x^{2} + 4 = 24$