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Chapter 9: Q.9.11 (page 865)

Solve3(a-3)2=54

Short Answer

Expert verified

The solutions of the quadratic equation:a=32+3,a=-32+3

Step by step solution

01

Step 1. Given information

Consider the quadratic equation

3(a-3)2=54

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

Ifx2=k, thenx=卤k

Divide both sides by the coefficient 3.

(a-3)2=543(a-3)2=18

Use the Square Root Property on the binomial.

a-3=卤18

02

Step 2. Simplify the radical expression.

Simplify the radical and solve for a.

role="math" localid="1645375659594" a=卤9路2+3a=卤32+3

Rewrite to show two solutions.

a=32+3,a=-32+3

03

Step 3. Check the solutions:  

Substitute a=32+3in the original equation.

role="math" localid="1645376089377" 3(a-3)2=543(32+3-3)2=?543(32)2=?543(18)=?5454=54

Substitute a=-32+3in the original equation.

3(a-3)2=543(-32+3-3)2=?543(32)2=?543(18)=?5454=54

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