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Chapter 10: Q 254. (page 1236)

In the following exercises, solve by completing the square.

w2-20w=100

Short Answer

Expert verified

The solutions arew=-102+10andw=102+10.

Step by step solution

01

Given information. 

The given equation isw2-20w=100

02

Make the perfect square.

Add 100 to both sides of the equation.

w2-20w+100=200

Writing it as a binomial square.

w2-2脳w脳10+102=200(w-10)2=200

03

Use the square root property. 

w-10=卤200w-10=卤100脳2w-10=卤100脳2w-10=卤102

The two equations arew-10=102andw-10=-102.

04

Solve both equations for w.

w-10=102w=102+10Orw-10=-102w=-102+10

Therefore, the solutions are w=-102+10andw=102+10.

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