Question

How do you solve `x^2 = -5x - 5`?

Answer 1

`x = (-5 +- sqrt5)/2`

Explanation:

First, bring the equation to standard form:
`y = x^2 + 5x + 5 = 0`
Use the improved quadratic formula (Google Search)
`D = d^2 = b^2 - 4ac = 25 - 20 = 5` --> `d = +- sqrt5`
There are 2 real roots:
`x = -b/(2a) +- d/(2a) = -5/2 +- sqrt5/2 = (-5 +- sqrt5)/2`