x^2+19x+37=

Solution for x^2+19x+37= equation:

Simplifying
x2 + 19x + 37 = 0

Reorder the terms:
37 + 19x + x2 = 0

Solving
37 + 19x + 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 + 19x + -37 + x2 = 0 + -37

Reorder the terms:
37 + -37 + 19x + x2 = 0 + -37

Combine like terms: 37 + -37 = 0
0 + 19x + x2 = 0 + -37
19x + x2 = 0 + -37

Combine like terms: 0 + -37 = -37
19x + x2 = -37

The x term is 19x.  Take half its coefficient (9.5).
Square it (90.25) and add it to both sides.

Add '90.25' to each side of the equation.
19x + 90.25 + x2 = -37 + 90.25

Reorder the terms:
90.25 + 19x + x2 = -37 + 90.25

Combine like terms: -37 + 90.25 = 53.25
90.25 + 19x + x2 = 53.25

Factor a perfect square on the left side:
(x + 9.5)(x + 9.5) = 53.25

Calculate the square root of the right side: 7.29725976

Break this problem into two subproblems by setting 
(x + 9.5) equal to 7.29725976 and -7.29725976.

Subproblem 1
x + 9.5 = 7.29725976

Simplifying
x + 9.5 = 7.29725976

Reorder the terms:
9.5 + x = 7.29725976

Solving
9.5 + x = 7.29725976

Solving for variable 'x'.

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

Add '-9.5' to each side of the equation.
9.5 + -9.5 + x = 7.29725976 + -9.5

Combine like terms: 9.5 + -9.5 = 0.0
0.0 + x = 7.29725976 + -9.5
x = 7.29725976 + -9.5

Combine like terms: 7.29725976 + -9.5 = -2.20274024
x = -2.20274024

Simplifying
x = -2.20274024

Subproblem 2
x + 9.5 = -7.29725976

Simplifying
x + 9.5 = -7.29725976

Reorder the terms:
9.5 + x = -7.29725976

Solving
9.5 + x = -7.29725976

Solving for variable 'x'.

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

Add '-9.5' to each side of the equation.
9.5 + -9.5 + x = -7.29725976 + -9.5

Combine like terms: 9.5 + -9.5 = 0.0
0.0 + x = -7.29725976 + -9.5
x = -7.29725976 + -9.5

Combine like terms: -7.29725976 + -9.5 = -16.79725976
x = -16.79725976

Simplifying
x = -16.79725976

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.20274024, -16.79725976}