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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. 18 (page 869)

In the following exercises, solve each equation.
$\frac{3}{2} b^{2} 鈭� 7 = 41$

Short Answer

Expert verified

The solution of the equation is $b = 4 \sqrt{2}, - 4 \sqrt{2}$

Step by step solution

01

Step 1. Given information

In the given question we have to solve given equation.
$\frac{3}{2} b^{2} 鈭� 7 = 41$

02

Step 2. The given equation is 32b2−7=41

Isolate the quadratic term.

Add 7 on both side

$\frac{3}{2} b^{2} 鈭� 7 + 7 = 41 + 7 \frac{3}{2} b^{2} = 48$

Multiply by $\frac{2}{3}$ on both side

$\frac{3}{2} b^{2} 脳 \frac{2}{3} = 48 脳 \frac{2}{3} b^{2} = 16 脳 2$

03

Step 3. Use the Square Root Property.

$b = 卤 \sqrt{16 脳 2}$

Simplify the radical.

$b = 卤 4 \sqrt{2}$

04

Step 4. Rewrite to show two solutions.

$b = 4 \sqrt{2} b = - 4 \sqrt{2}$

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