2x^2+10x+37=169

Solution for 2x^2+10x+37=169 equation:

Simplifying
2x2 + 10x + 37 = 169

Reorder the terms:
37 + 10x + 2x2 = 169

Solving
37 + 10x + 2x2 = 169

Solving for variable 'x'.

Reorder the terms:
37 + -169 + 10x + 2x2 = 169 + -169

Combine like terms: 37 + -169 = -132
-132 + 10x + 2x2 = 169 + -169

Combine like terms: 169 + -169 = 0
-132 + 10x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-66 + 5x + x2) = 0

Factor a trinomial.
2((-11 + -1x)(6 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-11 + -1x)' equal to zero and attempt to solve:

Simplifying
-11 + -1x = 0

Solving
-11 + -1x = 0

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

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

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

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

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

Simplifying
x = -11
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-11, 6}