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Chapter 6: Q 283 (page 627)

In the following exercises, solve:

5a2鈭�26a=24

Short Answer

Expert verified

The solutions are a=6anda=-45.

Step by step solution

01

Step 1. Given Information

The given quadratic equation is 5a2-26a=24.

We have to solve the quadratic equation by factoring.

02

Step 2. Factor the quadratic expression

First, write the given equation in standard form.

The standard form of the quadratic equation is

ax2+bx+c=0

Therefore,

5a2鈭�26a=245a2-26a-24=0

Now, let's factor the quadratic expression

5a2-26a-24=05a2-30a+4a-24=05a(a-6)+4(a-6)=0(5a+4)(a-6)=0

03

Step 3. Use the Zero Product Property  

The equations we get are

5a+4=0a-6=0

Thus,

5a+4=0a=-45ora-6=0a=6

04

Step 4. Verify the answers

To verify the answer we will substitute the solutions separately into the original equation.

Put a=6in the given equation,

5(6)2-26(6)=245(36)-156=24180-156=2424=24

This is true.

Now, put a=-45in the given equation

5(-45)2-26(-45)=24165+1045=2424=24

This is true.

Hence, the solutions area=6,-45.

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