x^2 = -13x - 4x2=−13x−4
Subtract -13x - 4−13x−4 from both sides:
x^2 + 13x + 4 = 0x2+13x+4=0
Since it doesn't neatly factor, one of the simplest ways to calculate it is the quadratic formula:
x = (-b+-sqrt(b^2-4ac))/(2a)x=−b±√b2−4ac2a where aa is the coefficient of x^2x2, bb is the coefficient of xx, cc is the constant.
Substitute the values for a (1)a(1), b (13)b(13), and c (4)c(4)...
x = (-(13)+-sqrt((13)^2-4(1)(4)))/(2(1))x=−(13)±√(13)2−4(1)(4)2(1)
x = (-13+-sqrt(153))/2x=−13±√1532
sqrt(153)√153 can also be represented as 3*sqrt(17)3⋅√17 (because
sqrt(153) = sqrt(9 * 17) = sqrt(3^2 * 17)√153=√9⋅17=√32⋅17), so it could also be shown as
x = (-13+-3sqrt(17))/2x=−13±3√172