Question

How do you solve `x^ { 2} + 12x = - 60`?

Answer 1

Use the quadratic equation

Explanation:

First we need to add 60 to make the right-hand side 0:
`x^2+12x+60=0`
Since this quadratic equation is not factorable, we apply the quadratic equation:
`x=(-12+-sqrt(12^2-4*1*60))/(2*1)`
`x=(-12+-sqrt(-96))/2`
Since we cannot square root a negative value, we use `i` to denote `sqrt(-1)` as the imaginary number
`x=-6+-(4isqrt(6))/2`
`x=-6+-2isqrt(6)`
Therefore, our answers are `x=-6+2isqrt(6)` and `x=-6-2isqrt(6)`

Answer 2

`x=-6+-isqrt(-24)`

Explanation:

Give -

`x^2+12x=-60`

Let use completing the square method

`x^2+12x+36=-60+36`

`(x+6)^2=-24`

`x+6=+-isqrt(-24)`

`x=-6+-isqrt(-24)`