x^2+38x+217=25

Solution for x^2+38x+217=25 equation:

Simplifying
x2 + 38x + 217 = 25

Reorder the terms:
217 + 38x + x2 = 25

Solving
217 + 38x + x2 = 25

Solving for variable 'x'.

Reorder the terms:
217 + -25 + 38x + x2 = 25 + -25

Combine like terms: 217 + -25 = 192
192 + 38x + x2 = 25 + -25

Combine like terms: 25 + -25 = 0
192 + 38x + x2 = 0

Factor a trinomial.
(32 + x)(6 + x) = 0

Subproblem 1
Set the factor '(32 + x)' equal to zero and attempt to solve:

Simplifying
32 + x = 0

Solving
32 + x = 0

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

Add '-32' to each side of the equation.
32 + -32 + x = 0 + -32

Combine like terms: 32 + -32 = 0
0 + x = 0 + -32
x = 0 + -32

Combine like terms: 0 + -32 = -32
x = -32

Simplifying
x = -32
Subproblem 2
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 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 + x = 0 + -6

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

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

Simplifying
x = -6
Solution
x = {-32, -6}