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Chapter 9: Q. 9.7 (page 863)

Solve12x2+4=24

Short Answer

Expert verified

The solutions of the quadratic equation:x=210,x=-210

Step by step solution

01

Step 1. Given information

Consider the quadratic equation

12x2+4=24

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

Ifx2=k, thenx=卤k

Isolate the quadratic term.

12x2=24-412x2=20

Multiply by 21to make the coefficient 1.

21路12x2=21路20x2=40

Use the Square Root Property.

x=卤40

02

Step 2. Simplify the expression.  

Simplify the radical.

x=卤10路4x=卤210

Rewrite to show two solutions.

x=210,x=-210

03

Step 3. Check the solutions:  

Substitute x=210in the original solution.

role="math" localid="1645359951214" 12x2+4=2412(210)2+4=?2412(40)+4=?2424=24

Substitute x=-210in the original solution.

12x2+4=2412(-210)2+4=?2412(40)+4=?2424=24

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