Q.9.17 Solve聽(3r+4)2=-8... [FREE SOLUTION]

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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 9: Q.9.17 (page 867)

Solve ${(3 r + 4)}^{2} = - 8$

Short Answer

Expert verified

The solutions are $r = - \frac{4}{3} + i \frac{2 \sqrt{2}}{3}, r = - \frac{4}{3} - i \frac{2 \sqrt{2}}{3}$

Step by step solution

Step 1. Given information

Consider the quadratic equation ${(3 r + 4)}^{2} = - 8$

Use the Square Root Property and simplify the radical.

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

$(3 r + 4) = 卤 \sqrt{- 8} (3 r + 4) = 卤 \sqrt{8} i (3 r + 4) = 卤 \sqrt{4 路 2} i (3 r + 4) = 卤 2 \sqrt{2} i$

Subtract 4 from both sides.

$3 r = 卤 2 \sqrt{2} i - 4$

Divide both sides by 3.

$r = \frac{卤 2 \sqrt{2} i - 4}{3}$

Rewrite in standard form.

$r = 卤 \frac{2 \sqrt{2}}{3} i - \frac{4}{3}$

Rewrite to show two solutions.

localid="1645459017698" $r = \frac{2 \sqrt{2}}{3} i - \frac{4}{3}, r = - \frac{2 \sqrt{2}}{3} i - \frac{4}{3}$

Step 2. Check for solutions.

Substitute $r = \frac{2 \sqrt{2}}{3} i - \frac{4}{3}$ in the original equation.

${(3 r + 4)}^{2} = - 8 {(3 (\frac{2 \sqrt{2}}{3} i - \frac{4}{3}) + 4)}^{2} \overset{?}{=} - 8 {(- 2 \sqrt{2} - 4 + 4)}^{2} \overset{?}{=} - 8 - 4 路 2 \overset{?}{=} - 8 - 8 = - 8$

Substitute $r = - \frac{2 \sqrt{2}}{3} i - \frac{4}{3}$ in the original equation.

${(3 r + 4)}^{2} = - 8 {(3 (- \frac{2 \sqrt{2}}{3} i - \frac{4}{3}) + 4)}^{2} \overset{?}{=} - 8 {(- 2 \sqrt{2} - 4 + 4)}^{2} \overset{?}{=} - 8 - 4 路 2 \overset{?}{=} - 8 - 8 = - 8$

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91影视

Solve ${(3 r + 4)}^{2} = - 8$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Check for solutions.

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91影视

Solve(3r+4)2=-8

Short Answer

Step by step solution

Step 1. Given information

Step 2. Check for solutions.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Geometry

Applied Mathematics

Probability and Statistics

Pure Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Solve ${(3 r + 4)}^{2} = - 8$