Question

How do you solve `|y^ { 2} - 84| = 5y`?

Answer 1

See below.

Explanation:

`|y^ { 2} - 84| = 5y`

`y^ { 2} - 84 = 5y` and `y^ { 2} - 84 = -5y`

So, we set up two quadratics.

`y^ { 2} -5y- 84 =0`
`(y-12)(y+7)=0`
`y=12,-7`

`y^ { 2}+5y- 84 =0`
`(y+12)(y-7)=0`
`y=-12,7`

However, since the function is absolute, the right hand side cannot be negative. So, only positive values of `y` work, namely `12, 7`.