Question 761571
{{{x^2 + 11*x = -30}}}

Can be written as:

{{{x^2 + 11*x + 30 = 0}}}

If the two roots are -a and -b, then (x + a)*(x + b) = 0

x^2 + (a+b) x + ab = 0.

Comparing it with your equation,

a + b = 11
a * b = 30

One way to find out a and b is through trial and error, by looking at all factors of 30 that sum up to 11. We get the combination of 6 and 5.

So the equation can be written as

{{{x^2 + 6*x + 5*x + 30 = 0}}}

{{{x * (x + 6) + 5 * (x + 6) = 0}}}

{{{(x + 6) * (x + 5) = 0}}}

{{{ x = -6 }}} or {{{ x = -5}}}

Roots are -6 and -5.

You can also solve it using the standard quadratic solver.

*[invoke quadratic "x", 1, 11, 30]