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Chapter 9: Q.9.15 (page 866)

Solve5(a-5)2+4=104

Short Answer

Expert verified

The solutions of the quadratic equation a=25+5,a=-25+5

Step by step solution

01

Step 1. Given information

Consider the quadratic equation

5(a-5)2+4=104

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

Ifx2=k, thenx=卤k

Subtract 4 from both sides to isolate the binomial term.

5(a-5)2=104-45(a-5)2=100

Divide both sides by 5.

(a-5)2=20

Use the Square Root Property.

(a-5)=卤20

02

Step 2. Simplify the radical expression.

Simplify the radical and solve for a.

a-5=卤4路5a=卤25+5

Rewrite to show two solutions.

a=25+5,a=-25+5

03

Step 3. Check the solutions.

Substitute a=25+5in the original equation.

role="math" localid="1645452752302" 5(a-5)2+4=1045(25+5-5)2+4=?1045(4路5)+4=?104100+4=?104104=104

Substitute a=-25+5in the original equation.

5(a-5)2+4=1045(-25+5-5)2+4=?1045(4路5)+4=?104100+4=?104104=104

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Solve by using the Quadratic Formula:r2+10r+25=0

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