x^2-4x-90=0

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Solution for x^2-4x-90=0 equation: 


Simplifying
x2 + -4x + -90 = 0

Reorder the terms:
-90 + -4x + x2 = 0

Solving
-90 + -4x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '90' to each side of the equation.
-90 + -4x + 90 + x2 = 0 + 90

Reorder the terms:
-90 + 90 + -4x + x2 = 0 + 90

Combine like terms: -90 + 90 = 0
0 + -4x + x2 = 0 + 90
-4x + x2 = 0 + 90

Combine like terms: 0 + 90 = 90
-4x + x2 = 90

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 = 90 + 4

Reorder the terms:
4 + -4x + x2 = 90 + 4

Combine like terms: 90 + 4 = 94
4 + -4x + x2 = 94

Factor a perfect square on the left side:
(x + -2)(x + -2) = 94

Calculate the square root of the right side: 9.695359715

Break this problem into two subproblems by setting 
(x + -2) equal to 9.695359715 and -9.695359715.


Subproblem 1
x + -2 = 9.695359715

Simplifying
x + -2 = 9.695359715

Reorder the terms:
-2 + x = 9.695359715

Solving
-2 + x = 9.695359715

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 = 9.695359715 + 2

Combine like terms: -2 + 2 = 0
0 + x = 9.695359715 + 2
x = 9.695359715 + 2

Combine like terms: 9.695359715 + 2 = 11.695359715
x = 11.695359715

Simplifying
x = 11.695359715


Subproblem 2
x + -2 = -9.695359715

Simplifying
x + -2 = -9.695359715

Reorder the terms:
-2 + x = -9.695359715

Solving
-2 + x = -9.695359715

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 = -9.695359715 + 2

Combine like terms: -2 + 2 = 0
0 + x = -9.695359715 + 2
x = -9.695359715 + 2

Combine like terms: -9.695359715 + 2 = -7.695359715
x = -7.695359715

Simplifying
x = -7.695359715


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.695359715, -7.695359715}

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