X*X+37=14X-8

Solution for X*X+37=14X-8 equation:

Simplifying
X * X + 37 = 14X + -8

Multiply X * X
X2 + 37 = 14X + -8

Reorder the terms:
37 + X2 = 14X + -8

Reorder the terms:
37 + X2 = -8 + 14X

Solving
37 + X2 = -8 + 14X

Solving for variable 'X'.

Reorder the terms:
37 + 8 + -14X + X2 = -8 + 14X + 8 + -14X

Combine like terms: 37 + 8 = 45
45 + -14X + X2 = -8 + 14X + 8 + -14X

Reorder the terms:
45 + -14X + X2 = -8 + 8 + 14X + -14X

Combine like terms: -8 + 8 = 0
45 + -14X + X2 = 0 + 14X + -14X
45 + -14X + X2 = 14X + -14X

Combine like terms: 14X + -14X = 0
45 + -14X + X2 = 0

Factor a trinomial.
(5 + -1X)(9 + -1X) = 0

Subproblem 1
Set the factor '(5 + -1X)' equal to zero and attempt to solve:

Simplifying
5 + -1X = 0

Solving
5 + -1X = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1X = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1X = 0 + -5
-1X = 0 + -5

Combine like terms: 0 + -5 = -5
-1X = -5

Divide each side by '-1'.
X = 5

Simplifying
X = 5
Subproblem 2
Set the factor '(9 + -1X)' equal to zero and attempt to solve:

Simplifying
9 + -1X = 0

Solving
9 + -1X = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1X = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1X = 0 + -9
-1X = 0 + -9

Combine like terms: 0 + -9 = -9
-1X = -9

Divide each side by '-1'.
X = 9

Simplifying
X = 9
Solution
X = {5, 9}