x^2-37x+40=0

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Solution for x^2-37x+40=0 equation: 


Simplifying
x2 + -37x + 40 = 0

Reorder the terms:
40 + -37x + x2 = 0

Solving
40 + -37x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-40' to each side of the equation.
40 + -37x + -40 + x2 = 0 + -40

Reorder the terms:
40 + -40 + -37x + x2 = 0 + -40

Combine like terms: 40 + -40 = 0
0 + -37x + x2 = 0 + -40
-37x + x2 = 0 + -40

Combine like terms: 0 + -40 = -40
-37x + x2 = -40

The x term is -37x.  Take half its coefficient (-18.5).
Square it (342.25) and add it to both sides.

Add '342.25' to each side of the equation.
-37x + 342.25 + x2 = -40 + 342.25

Reorder the terms:
342.25 + -37x + x2 = -40 + 342.25

Combine like terms: -40 + 342.25 = 302.25
342.25 + -37x + x2 = 302.25

Factor a perfect square on the left side:
(x + -18.5)(x + -18.5) = 302.25

Calculate the square root of the right side: 17.385338651

Break this problem into two subproblems by setting 
(x + -18.5) equal to 17.385338651 and -17.385338651.


Subproblem 1
x + -18.5 = 17.385338651

Simplifying
x + -18.5 = 17.385338651

Reorder the terms:
-18.5 + x = 17.385338651

Solving
-18.5 + x = 17.385338651

Solving for variable 'x'.

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

Add '18.5' to each side of the equation.
-18.5 + 18.5 + x = 17.385338651 + 18.5

Combine like terms: -18.5 + 18.5 = 0.0
0.0 + x = 17.385338651 + 18.5
x = 17.385338651 + 18.5

Combine like terms: 17.385338651 + 18.5 = 35.885338651
x = 35.885338651

Simplifying
x = 35.885338651


Subproblem 2
x + -18.5 = -17.385338651

Simplifying
x + -18.5 = -17.385338651

Reorder the terms:
-18.5 + x = -17.385338651

Solving
-18.5 + x = -17.385338651

Solving for variable 'x'.

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

Add '18.5' to each side of the equation.
-18.5 + 18.5 + x = -17.385338651 + 18.5

Combine like terms: -18.5 + 18.5 = 0.0
0.0 + x = -17.385338651 + 18.5
x = -17.385338651 + 18.5

Combine like terms: -17.385338651 + 18.5 = 1.114661349
x = 1.114661349

Simplifying
x = 1.114661349


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {35.885338651, 1.114661349}

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