x^2-4x-37=0

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Solution for x^2-4x-37=0 equation: 


Simplifying
x2 + -4x + -37 = 0

Reorder the terms:
-37 + -4x + x2 = 0

Solving
-37 + -4x + 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 + -4x + 37 + x2 = 0 + 37

Reorder the terms:
-37 + 37 + -4x + x2 = 0 + 37

Combine like terms: -37 + 37 = 0
0 + -4x + x2 = 0 + 37
-4x + x2 = 0 + 37

Combine like terms: 0 + 37 = 37
-4x + x2 = 37

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 37 + 4

Reorder the terms:
4 + -4x + x2 = 37 + 4

Combine like terms: 37 + 4 = 41
4 + -4x + x2 = 41

Factor a perfect square on the left side:
(x + -2)(x + -2) = 41

Calculate the square root of the right side: 6.403124237

Break this problem into two subproblems by setting 
(x + -2) equal to 6.403124237 and -6.403124237.


Subproblem 1
x + -2 = 6.403124237

Simplifying
x + -2 = 6.403124237

Reorder the terms:
-2 + x = 6.403124237

Solving
-2 + x = 6.403124237

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 6.403124237 + 2

Combine like terms: -2 + 2 = 0
0 + x = 6.403124237 + 2
x = 6.403124237 + 2

Combine like terms: 6.403124237 + 2 = 8.403124237
x = 8.403124237

Simplifying
x = 8.403124237


Subproblem 2
x + -2 = -6.403124237

Simplifying
x + -2 = -6.403124237

Reorder the terms:
-2 + x = -6.403124237

Solving
-2 + x = -6.403124237

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -6.403124237 + 2

Combine like terms: -2 + 2 = 0
0 + x = -6.403124237 + 2
x = -6.403124237 + 2

Combine like terms: -6.403124237 + 2 = -4.403124237
x = -4.403124237

Simplifying
x = -4.403124237


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.403124237, -4.403124237}

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