Question

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

Answer 1

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`

Answer 2

`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`