Chapter 11: Q. 9.12 (page 1069)

Solve $2 {(b + 2)}^{2} = 80$

Short Answer

Expert verified

The solutions are $b = 2 \sqrt{10} - 2, b = - 2 \sqrt{10} - 2$

Step by step solution

Step 1. Given information

Consider the quadratic equation

$2 {(b + 2)}^{2} = 80$

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

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

Divide both sides by the coefficient 2.

localid="1663771543619" ${(b + 2)}^{2} = \frac{80}{2} = 40$

Use the square root property on the binomial.

$b + 2 = \pm \sqrt{40}$

Step 2. Simplify the radical expression.

Simplify the radical and solve for $b$ .

$b = \pm \sqrt{4 \cdot 10} - 2 b = \pm 2 \sqrt{10} - 2$

Rewrite to show two solutions.

$b = 2 \sqrt{10} - 2, b = - 2 \sqrt{10} - 2$

Step 3. Check the solutions:

Substitute $b = 2 \sqrt{10} - 2$ in the original equation.

role="math" localid="1645377113748" $2 {(b + 2)}^{2} = 80 2 {(2 \sqrt{10} - 2 + 2)}^{2} \overset{?}{=} 80 2 (40) \overset{?}{=} 80 80 = 80$

Substitute $b = - 2 \sqrt{10} - 2$ in the original equation.

$2 {(b + 2)}^{2} = 80 2 {(- 2 \sqrt{10} - 2 + 2)}^{2} \overset{?}{=} 80 2 (40) \overset{?}{=} 80 80 = 80$

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Solve $2 {(b + 2)}^{2} = 80$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Simplify the radical expression.

Step 3. Check the solutions:

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Solve2(b+2)2=80

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

Statistics

Applied Mathematics

Mechanics Maths

Geometry

Pure Maths

Decision Maths

Study anywhere. Anytime. Across all devices.

Solve $2 {(b + 2)}^{2} = 80$