x^2-(0.25x)-5=0

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Solution for x^2-(0.25x)-5=0 equation: 


Simplifying
x2 + -1(0.25x) + -5 = 0

Remove parenthesis around (0.25x)
x2 + -1 * 0.25x + -5 = 0

Multiply -1 * 0.25
x2 + -0.25x + -5 = 0

Reorder the terms:
-5 + -0.25x + x2 = 0

Solving
-5 + -0.25x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -0.25x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + -0.25x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -0.25x + x2 = 0 + 5
-0.25x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
-0.25x + x2 = 5

The x term is -0.25x.  Take half its coefficient (-0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
-0.25x + 0.015625 + x2 = 5 + 0.015625

Reorder the terms:
0.015625 + -0.25x + x2 = 5 + 0.015625

Combine like terms: 5 + 0.015625 = 5.015625
0.015625 + -0.25x + x2 = 5.015625

Factor a perfect square on the left side:
(x + -0.125)(x + -0.125) = 5.015625

Calculate the square root of the right side: 2.239559108

Break this problem into two subproblems by setting 
(x + -0.125) equal to 2.239559108 and -2.239559108.


Subproblem 1
x + -0.125 = 2.239559108

Simplifying
x + -0.125 = 2.239559108

Reorder the terms:
-0.125 + x = 2.239559108

Solving
-0.125 + x = 2.239559108

Solving for variable 'x'.

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

Add '0.125' to each side of the equation.
-0.125 + 0.125 + x = 2.239559108 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + x = 2.239559108 + 0.125
x = 2.239559108 + 0.125

Combine like terms: 2.239559108 + 0.125 = 2.364559108
x = 2.364559108

Simplifying
x = 2.364559108


Subproblem 2
x + -0.125 = -2.239559108

Simplifying
x + -0.125 = -2.239559108

Reorder the terms:
-0.125 + x = -2.239559108

Solving
-0.125 + x = -2.239559108

Solving for variable 'x'.

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

Add '0.125' to each side of the equation.
-0.125 + 0.125 + x = -2.239559108 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + x = -2.239559108 + 0.125
x = -2.239559108 + 0.125

Combine like terms: -2.239559108 + 0.125 = -2.114559108
x = -2.114559108

Simplifying
x = -2.114559108


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.364559108, -2.114559108}

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