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Chapter 11: Q.9.16 (page 1069)

Solve3(b+3)2-8=88

Short Answer

Expert verified

The solutions of the quadratic equation:b=42-3,b=-42-3

Step by step solution

01

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.

Ifx2=k, thenx=卤k

Add 8 from both sides to isolate the binomial term.

localid="1645453235551" 3(b+3)2=88+83(b+3)2=96

Divide both sides by 3.

localid="1663772006219" (b+3)2=963=32

Use the Square Root Property.

(b+3)=卤32

02

Step 2. Simplify the radical expression. 

Simplify the radical and solve for b.

b+3=卤16路2b=卤42-3

Rewrite to show two solutions.

b=42-3,b=-42-3

03

Step 3. Check the solutions. 

Substitute b=42-3in the original equation.

role="math" localid="1645453786181" 3(b+3)2-8=883(42-3+3)2-8=?883(16路2)-8=?8896-8=?8888=88

Substitute b=-42-3in the original equation.

3(b+3)2-8=883(-42-3+3)2-8=?883(16路2)-8=?8896-8=?8888=88

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