x^2+25x+37=

Solution for x^2+25x+37= equation:

Simplifying
x2 + 25x + 37 = 0

Reorder the terms:
37 + 25x + x2 = 0

Solving
37 + 25x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-37' to each side of the equation.
37 + 25x + -37 + x2 = 0 + -37

Reorder the terms:
37 + -37 + 25x + x2 = 0 + -37

Combine like terms: 37 + -37 = 0
0 + 25x + x2 = 0 + -37
25x + x2 = 0 + -37

Combine like terms: 0 + -37 = -37
25x + x2 = -37

The x term is 25x.  Take half its coefficient (12.5).
Square it (156.25) and add it to both sides.

Add '156.25' to each side of the equation.
25x + 156.25 + x2 = -37 + 156.25

Reorder the terms:
156.25 + 25x + x2 = -37 + 156.25

Combine like terms: -37 + 156.25 = 119.25
156.25 + 25x + x2 = 119.25

Factor a perfect square on the left side:
(x + 12.5)(x + 12.5) = 119.25

Calculate the square root of the right side: 10.920164834

Break this problem into two subproblems by setting 
(x + 12.5) equal to 10.920164834 and -10.920164834.

Subproblem 1
x + 12.5 = 10.920164834

Simplifying
x + 12.5 = 10.920164834

Reorder the terms:
12.5 + x = 10.920164834

Solving
12.5 + x = 10.920164834

Solving for variable 'x'.

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

Add '-12.5' to each side of the equation.
12.5 + -12.5 + x = 10.920164834 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + x = 10.920164834 + -12.5
x = 10.920164834 + -12.5

Combine like terms: 10.920164834 + -12.5 = -1.579835166
x = -1.579835166

Simplifying
x = -1.579835166

Subproblem 2
x + 12.5 = -10.920164834

Simplifying
x + 12.5 = -10.920164834

Reorder the terms:
12.5 + x = -10.920164834

Solving
12.5 + x = -10.920164834

Solving for variable 'x'.

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

Add '-12.5' to each side of the equation.
12.5 + -12.5 + x = -10.920164834 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + x = -10.920164834 + -12.5
x = -10.920164834 + -12.5

Combine like terms: -10.920164834 + -12.5 = -23.420164834
x = -23.420164834

Simplifying
x = -23.420164834

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.579835166, -23.420164834}