x^2-4x-40=0

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Solution for x^2-4x-40=0 equation: 


Simplifying
x2 + -4x + -40 = 0

Reorder the terms:
-40 + -4x + x2 = 0

Solving
-40 + -4x + 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 + -4x + 40 + x2 = 0 + 40

Reorder the terms:
-40 + 40 + -4x + x2 = 0 + 40

Combine like terms: -40 + 40 = 0
0 + -4x + x2 = 0 + 40
-4x + x2 = 0 + 40

Combine like terms: 0 + 40 = 40
-4x + x2 = 40

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 = 40 + 4

Reorder the terms:
4 + -4x + x2 = 40 + 4

Combine like terms: 40 + 4 = 44
4 + -4x + x2 = 44

Factor a perfect square on the left side:
(x + -2)(x + -2) = 44

Calculate the square root of the right side: 6.633249581

Break this problem into two subproblems by setting 
(x + -2) equal to 6.633249581 and -6.633249581.


Subproblem 1
x + -2 = 6.633249581

Simplifying
x + -2 = 6.633249581

Reorder the terms:
-2 + x = 6.633249581

Solving
-2 + x = 6.633249581

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 = 6.633249581 + 2

Combine like terms: -2 + 2 = 0
0 + x = 6.633249581 + 2
x = 6.633249581 + 2

Combine like terms: 6.633249581 + 2 = 8.633249581
x = 8.633249581

Simplifying
x = 8.633249581


Subproblem 2
x + -2 = -6.633249581

Simplifying
x + -2 = -6.633249581

Reorder the terms:
-2 + x = -6.633249581

Solving
-2 + x = -6.633249581

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 = -6.633249581 + 2

Combine like terms: -2 + 2 = 0
0 + x = -6.633249581 + 2
x = -6.633249581 + 2

Combine like terms: -6.633249581 + 2 = -4.633249581
x = -4.633249581

Simplifying
x = -4.633249581


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.633249581, -4.633249581}

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