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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.2 (page 869)

Solve Quadratic Equations of the Form $a x^{2} = k$ Using the Square Root Property.
In the following exercises, solve each equation $b^{2} = 144$

Short Answer

Expert verified

The solution of the quadratic equation:

$b = 12, b = - 12$

Step by step solution

01

Step 1. Given information

Consider the quadratic equation $b^{2} = 144$

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

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

So, $b = 卤 \sqrt{144}$

Simplify the radical.

$b = 卤 \sqrt{12 路 12} b = 卤 12$

Rewrite to show two solutions.

$b = 12, b = - 12$

02

Step 2. Check the solutions

Substitute $b = 12$ in the original equation

role="math" localid="1645621359539" $b^{2} = 144 {(12)}^{2} \overset{?}{=} 144 144 = 144$

Substitute $b = - 12$ in the original equation.

$b^{2} = 144 {(- 12)}^{2} \overset{?}{=} 144 144 = 144$

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Most popular questions from this chapter

Solve quadratic equation $36 x^{2} - 24 x + 4 = 81$ using square root property

In the following exercise, solve by completing the square.

$x^{2} - 20 x = 21$

Identify the most appropriate method to use to solve each quadratic equation.

$a) 8 a^{2} + 3 a - 9 = 0 b) 4 b^{2} + 4 b + 1 = 0 c) 5 c^{2} = 125$

In the following exercise, solve by completing the square.

$z^{2} + 12 z = - 11$

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