x^2+17x-37=0

Solution for x^2+17x-37=0 equation:

Simplifying
x2 + 17x + -37 = 0

Reorder the terms:
-37 + 17x + x2 = 0

Solving
-37 + 17x + 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 + 17x + 37 + x2 = 0 + 37

Reorder the terms:
-37 + 37 + 17x + x2 = 0 + 37

Combine like terms: -37 + 37 = 0
0 + 17x + x2 = 0 + 37
17x + x2 = 0 + 37

Combine like terms: 0 + 37 = 37
17x + x2 = 37

The x term is 17x.  Take half its coefficient (8.5).
Square it (72.25) and add it to both sides.

Add '72.25' to each side of the equation.
17x + 72.25 + x2 = 37 + 72.25

Reorder the terms:
72.25 + 17x + x2 = 37 + 72.25

Combine like terms: 37 + 72.25 = 109.25
72.25 + 17x + x2 = 109.25

Factor a perfect square on the left side:
(x + 8.5)(x + 8.5) = 109.25

Calculate the square root of the right side: 10.45227248

Break this problem into two subproblems by setting 
(x + 8.5) equal to 10.45227248 and -10.45227248.

Subproblem 1
x + 8.5 = 10.45227248

Simplifying
x + 8.5 = 10.45227248

Reorder the terms:
8.5 + x = 10.45227248

Solving
8.5 + x = 10.45227248

Solving for variable 'x'.

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

Add '-8.5' to each side of the equation.
8.5 + -8.5 + x = 10.45227248 + -8.5

Combine like terms: 8.5 + -8.5 = 0.0
0.0 + x = 10.45227248 + -8.5
x = 10.45227248 + -8.5

Combine like terms: 10.45227248 + -8.5 = 1.95227248
x = 1.95227248

Simplifying
x = 1.95227248

Subproblem 2
x + 8.5 = -10.45227248

Simplifying
x + 8.5 = -10.45227248

Reorder the terms:
8.5 + x = -10.45227248

Solving
8.5 + x = -10.45227248

Solving for variable 'x'.

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

Add '-8.5' to each side of the equation.
8.5 + -8.5 + x = -10.45227248 + -8.5

Combine like terms: 8.5 + -8.5 = 0.0
0.0 + x = -10.45227248 + -8.5
x = -10.45227248 + -8.5

Combine like terms: -10.45227248 + -8.5 = -18.95227248
x = -18.95227248

Simplifying
x = -18.95227248

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.95227248, -18.95227248}