To solve the equation X^2 + X - 61 = -5, we need to simplify it first by adding 5 to both sides of the equation, which gives us X^2 + X - 56 = 0.
We can then use the quadratic formula to solve for X, which is:
X = (-b ± √(b^2 - 4ac)) / 2a
In this case, a = 1, b = 1, and c = -56.
Plugging these values into the quadratic formula, we get:
X = (-1 ± √(1^2 - 4(1)(-56))) / 2(1)
X = (-1 ± √(1 + 224)) / 2
X = (-1 ± √225) / 2
X = (-1 ± 15) / 2
So the two possible values of X are:
X = (-1 + 15) / 2 = 7
X = (-1 - 15) / 2 = -8
Therefore, X can be either 7 or -8.