x^2-5x-90=0

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Solution for x^2-5x-90=0 equation: 


Simplifying
x2 + -5x + -90 = 0

Reorder the terms:
-90 + -5x + x2 = 0

Solving
-90 + -5x + 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 + -5x + 90 + x2 = 0 + 90

Reorder the terms:
-90 + 90 + -5x + x2 = 0 + 90

Combine like terms: -90 + 90 = 0
0 + -5x + x2 = 0 + 90
-5x + x2 = 0 + 90

Combine like terms: 0 + 90 = 90
-5x + x2 = 90

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 90 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 90 + 6.25

Combine like terms: 90 + 6.25 = 96.25
6.25 + -5x + x2 = 96.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 96.25

Calculate the square root of the right side: 9.810708435

Break this problem into two subproblems by setting 
(x + -2.5) equal to 9.810708435 and -9.810708435.


Subproblem 1
x + -2.5 = 9.810708435

Simplifying
x + -2.5 = 9.810708435

Reorder the terms:
-2.5 + x = 9.810708435

Solving
-2.5 + x = 9.810708435

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 9.810708435 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 9.810708435 + 2.5
x = 9.810708435 + 2.5

Combine like terms: 9.810708435 + 2.5 = 12.310708435
x = 12.310708435

Simplifying
x = 12.310708435


Subproblem 2
x + -2.5 = -9.810708435

Simplifying
x + -2.5 = -9.810708435

Reorder the terms:
-2.5 + x = -9.810708435

Solving
-2.5 + x = -9.810708435

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -9.810708435 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -9.810708435 + 2.5
x = -9.810708435 + 2.5

Combine like terms: -9.810708435 + 2.5 = -7.310708435
x = -7.310708435

Simplifying
x = -7.310708435


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.310708435, -7.310708435}

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