How do you solve 5(x-7)^2=135?

2 Answers
Nityananda
Jun 5, 2017

12.2 & 1.8

Explanation:

Given, 5(x-7)^2=135

rArr x^2-14x+49=135/5

rArr x^2-14x+49-27=0

rArr x^2-14x+22=0

rArr x = [-b+-sqrt{b^2-4ac}]/[2a] [here b = -14, c=22 & a = 1]

rArr x = [-(-14)+-sqrt{(-14)^2-4*1*22}]/[2*1]

rArr x = [14+-sqrt(196-88)]/2

rArr x = [14 +-sqrt108]/2

rArr x = (14+-10.4)/2

rArr x = [14+10.4]/2 , [14-10.4]/2

rArr x = 12.2, 1.8

EZ as pi
Jun 5, 2017

x =12.196 or x = 1.804

Explanation:

Isolate the bracket that contains the x by dividing both sides by 5

(5(-7)^2)/5 = 135/5

(x-7)^2 = 27

Find the square root of both sides:

x-7 = +-sqrt27

Solve using the positive and negative roots:

x = +sqrt27 +7 = 12.196

x = -sqrt27+7 = 1.804

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