Question

How do you solve `3( x + 2)^{2} = 100`?

Answer 1

`x = -2+-(10sqrt(3))/3`

Explanation:

Multiply both sides by `3` to get:

`3^2(x+2)^2 = 100*3`

Take the square root of both sides, considering both positive and negative square roots to find:

`3(x+2) = +-10sqrt(3)`

Divide both sides by `3` to get:

`x+2 = +-(10sqrt(3))/3`

Subtract `2` from both sides to get:

`x = -2+-(10sqrt(3))/3`

Answer 2

`x=-2+-(10sqrt3)/3`

Explanation:

Given:`" "3(x+2)^2=100`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("With practice you will be able to do some of the")` `color(blue)("manipulation in your head, use shortcuts and generally be faster.")`

Divide both sides by 3

`(x+2)^2=100/3`

Square root both sides

`sqrt((x+2)^2) =sqrt100/sqrt3`

`x+2=+-10/sqrt3`

Mathematicians do not like to have a root in the denominator if they can help it. So lets get rid of it!

Write as: `" color(brown)(x+2=+-10/sqrt3color(blue)(xx1)`

but you may write 1 as: `" "1=sqrt3/sqrt3" "` giving:

`" color(brown)(x+2=+-10/sqrt3color(blue)(xxsqrt3/sqrt3)`

`x+2=+-(10sqrt(3))/3`

Subtract 2 from both sides

`x=+-(10sqrt3)/3-2`

`x=-2+-(10sqrt3)/3`