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Chapter 7: Q. 328 (page 893)

Solve Quadratic Equations by Factoring

In the following exercises, solve.

4b2+7b=-3

Short Answer

Expert verified

The solution isb=-34,-1.

Step by step solution

01

Step 1. Given Information  

We are given the quadratic equation4b2+7b=-3 and we need to solve it by factoring.

02

Step 2. Solving the quadratic  

Writing the quadratic equation in standard form:

4b2+7b=-3鈬�4b2+7b+3=0

Factoring the quadratic we get,

localid="1647785929270" 4b2+7b+3=0鈬�4b2+4b+3b+3=0鈬�4b(b+1)+3(b+1)=0鈬�4b+3b+1

Use the Zero Product Property to set each factor to 0,

4b+3=0鈬�4b=-3鈬�b=-34b+1=0鈬�b=-1

03

Step 3. Checking the answers  

Substituting each solution separately into the original equation:

b=-344b2+7b=-3鈬�4-342+7-34=-3鈬�4脳916-214-3鈬�94-214=-3鈬�-124=-3鈬�-3=-3b=-1,4b2+7b=-3鈬�4-12+7-1=-3鈬�4-7=-3鈬�-3=-3

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