Chapter 10: Q 10.9 (page 1159)

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

Short Answer

Expert verified

The solutions are $x = 2 \sqrt{10}, x = - 2 \sqrt{10}$ .

Step by step solution

Given Information.

The Given equation is $\frac{1}{2} x^{2} + 4 = 24$ .

Isolate the quadratic term and makes its coefficient one.

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

Divide both sides by $\frac{1}{2}$ .

$x^{2} = 20 \times 2 x^{2} = 40$

Use the square root property.

$x = \pm \sqrt{40}$

Simplify the radical by factoring the radicand.

$x = \pm \sqrt{2 \times 2 \times 2 \times 5}$

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

Rewrite to show two solutions.

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

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

Short Answer

Step by step solution

Given Information.

Isolate the quadratic term and makes its coefficient one.

Use the square root property.

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Solve12x2+4=24

Short Answer

Step by step solution

Given Information.

Isolate the quadratic term and makes its coefficient one.

Use the square root property.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Geometry

Calculus

Logic and Functions

Theoretical and Mathematical Physics

Decision Maths

Study anywhere. Anytime. Across all devices.

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