Chapter 11: Q.9.16 (page 1069)

Solve $3 {(b + 3)}^{2} - 8 = 88$

Short Answer

Expert verified

The solutions of the quadratic equation: $b = 4 \sqrt{2} - 3, b = - 4 \sqrt{2} - 3$

Step by step solution

Step 1. Given information

Consider the quadratic equation

$3 {(b + 3)}^{2} - 8 = 88$

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

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

Add 8 from both sides to isolate the binomial term.

localid="1645453235551" $3 {(b + 3)}^{2} = 88 + 8 3 {(b + 3)}^{2} = 96$

Divide both sides by 3.

localid="1663772006219" ${(b + 3)}^{2} = \frac{96}{3} = 32$

Use the Square Root Property.

$(b + 3) = \pm \sqrt{32}$

Step 2. Simplify the radical expression.

Simplify the radical and solve for $b$ .

$b + 3 = \pm \sqrt{16 \cdot 2} b = \pm 4 \sqrt{2} - 3$

Rewrite to show two solutions.

$b = 4 \sqrt{2} - 3, b = - 4 \sqrt{2} - 3$

Step 3. Check the solutions.

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

role="math" localid="1645453786181" $3 {(b + 3)}^{2} - 8 = 88 3 {(4 \sqrt{2} - 3 + 3)}^{2} - 8 \overset{?}{=} 88 3 (16 \cdot 2) - 8 \overset{?}{=} 88 96 - 8 \overset{?}{=} 88 88 = 88$

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

$3 {(b + 3)}^{2} - 8 = 88 3 {(- 4 \sqrt{2} - 3 + 3)}^{2} - 8 \overset{?}{=} 88 3 (16 \cdot 2) - 8 \overset{?}{=} 88 96 - 8 \overset{?}{=} 88 88 = 88$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Solve $3 {(b + 3)}^{2} - 8 = 88$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Simplify the radical expression.

Step 3. Check the solutions.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Mechanics Maths

Pure Maths

Theoretical and Mathematical Physics

Discrete Mathematics

Calculus

Study anywhere. Anytime. Across all devices.

Solve3(b+3)2-8=88

Short Answer

Step by step solution

Step 1. Given information

Step 2. Simplify the radical expression.

Step 3. Check the solutions.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Mechanics Maths

Pure Maths

Theoretical and Mathematical Physics

Discrete Mathematics

Calculus

Study anywhere. Anytime. Across all devices.

Solve $3 {(b + 3)}^{2} - 8 = 88$