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Chapter 10: Q 97 (page 1182)

Solve the equationx2+10x=-25:

(a) by using the Square Root Property

(b) by completing the square.

(c) Which method do you prefer? Why?

Short Answer

Expert verified

(a) The solution isx=-5.

(b) The solution is x=-5.

(c) The Square Root Property is preferred.

Step by step solution

01

Step 1. Given Information.

The equation is,

x2+10x=-25.

02

Part (a) Square root method

Given, x2+10x=-25.

Adding 25on both sides,

鈬�x2+10x+25=0

Factor the perfect square trinomial,

鈬�(x+5)2=0

Taking the square root property.

鈬�x+5=0鈬�x=-5

03

Part (b). Completing the square.

Given, x2+10x=-25

Adding the square of half of 10on both sides,

鈬�x2+10x+12102=-25+12102鈬�x2+10x+25=-25+25鈬�x2+10x+25=0

Taking the left side as a binomial square.

鈬�(x+5)2=0

Taking the square root on both sides,

鈬�x+5=0鈬�x=-5

04

Part (c). The better method.

The square root property is preferred because it is easier and most importantly a comparatively shorter method than completing the square.

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