a^2+a+8=118

Solution for a^2+a+8=118 equation:

Simplifying
a2 + a + 8 = 118

Reorder the terms:
8 + a + a2 = 118

Solving
8 + a + a2 = 118

Solving for variable 'a'.

Reorder the terms:
8 + -118 + a + a2 = 118 + -118

Combine like terms: 8 + -118 = -110
-110 + a + a2 = 118 + -118

Combine like terms: 118 + -118 = 0
-110 + a + a2 = 0

Factor a trinomial.
(-11 + -1a)(10 + -1a) = 0

Subproblem 1
Set the factor '(-11 + -1a)' equal to zero and attempt to solve:

Simplifying
-11 + -1a = 0

Solving
-11 + -1a = 0

Move all terms containing a to the left, all other terms to the right.

Add '11' to each side of the equation.
-11 + 11 + -1a = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -1a = 0 + 11
-1a = 0 + 11

Combine like terms: 0 + 11 = 11
-1a = 11

Divide each side by '-1'.
a = -11

Simplifying
a = -11
Subproblem 2
Set the factor '(10 + -1a)' equal to zero and attempt to solve:

Simplifying
10 + -1a = 0

Solving
10 + -1a = 0

Move all terms containing a to the left, all other terms to the right.

Add '-10' to each side of the equation.
10 + -10 + -1a = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1a = 0 + -10
-1a = 0 + -10

Combine like terms: 0 + -10 = -10
-1a = -10

Divide each side by '-1'.
a = 10

Simplifying
a = 10
Solution
a = {-11, 10}