Question

How do you solve `5(x+3/4)^2-2=43`?

Answer 1

`x=-15/4" or "x=9/4`

Explanation:

`"Isolate " (x+3/4)^2` on the left side of the equation.

add 2 to both sides.

`5(x+3/4)^2cancel(-2)cancel(+2)=43+2`

`rArr5(x+3/4)^2=45`

divide both sides by 5

`(cancel(5))/cancel(5)(x+3/4)^2=45/5`

`rArr(x+3/4)^2=9`

Take the `color(blue)"square root "` of both sides.

`sqrt((x+3/4)^2)=+-sqrt9`

`rArrx+3/4=+-3larrcolor(red)" 2 solutions"`

`color(blue)"Solution 1"`

`x=-3-3/4rArrx=-15/4`

`color(blue)"Solution 2"`

`x=+3-3/4=9/4`