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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 10: Q 10.19 (page 1162)

Solve $(a - 5)^{2} + 4 = 24$ .

Short Answer

Expert verified

The solutions are $a = 5 卤 2 \sqrt{5}$ .

Step by step solution

01

Given Information.

The Given equation is $(a - 5)^{2} + 4 = 24$ .

02

Isolate the binomial term.

$(a - 5)^{2} = 24 - 4 (a - 5)^{2} = 20$

03

Use the square root property.

$a - 5 = 卤 \sqrt{20}$

Factor the radicand.

$a - 5 = 卤 \sqrt{2 脳 2 脳 5} a - 5 = 卤 2 \sqrt{5}$

04

Solve for a.

$a = 5 卤 2 \sqrt{5}$

Rewrite to show two solutions.

$a = 5 + 2 \sqrt{5}, a = 5 - 2 \sqrt{5}$

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