Question

How do you solve `-x^2-12=-87`?

Answer 1

`x=+-5sqrt(3)`

Explanation:

If
`color(white)("XXX")-x^2-12=-87`
then
`color(white)("XXX")x^2+12=87`

`color(white)("XXX")x^2=75`

`color(white)("XXX")x=+-5sqrt(3)`

Answer 2

`x=+-5sqrt(3)`

Explanation:

Multiply all of both sides by (-1)

`+x^2+12=+87`

Subtract 12 from both sides

`x^2=87-12 = 75`

`x=sqrt(75)`

But 75 `->5xx15->5xx5xx3 = 5^2xx3`

`x=sqrt(5^2xx3)`

`x=5sqrt(3)` as an EXACT principle root answer (only positive)

However. This is a quadratic so it will have both positive and negative roots. The plot will cross the x-axis in 2 places

`x=+-5sqrt(3)`