x^2-.25x-16=0

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Solution for x^2-.25x-16=0 equation: 


Simplifying
x2 + -0.25x + -16 = 0

Reorder the terms:
-16 + -0.25x + x2 = 0

Solving
-16 + -0.25x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + -0.25x + 16 + x2 = 0 + 16

Reorder the terms:
-16 + 16 + -0.25x + x2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -0.25x + x2 = 0 + 16
-0.25x + x2 = 0 + 16

Combine like terms: 0 + 16 = 16
-0.25x + x2 = 16

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 = 16 + 0.015625

Reorder the terms:
0.015625 + -0.25x + x2 = 16 + 0.015625

Combine like terms: 16 + 0.015625 = 16.015625
0.015625 + -0.25x + x2 = 16.015625

Factor a perfect square on the left side:
(x + -0.125)(x + -0.125) = 16.015625

Calculate the square root of the right side: 4.001952648

Break this problem into two subproblems by setting 
(x + -0.125) equal to 4.001952648 and -4.001952648.


Subproblem 1
x + -0.125 = 4.001952648

Simplifying
x + -0.125 = 4.001952648

Reorder the terms:
-0.125 + x = 4.001952648

Solving
-0.125 + x = 4.001952648

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 = 4.001952648 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + x = 4.001952648 + 0.125
x = 4.001952648 + 0.125

Combine like terms: 4.001952648 + 0.125 = 4.126952648
x = 4.126952648

Simplifying
x = 4.126952648


Subproblem 2
x + -0.125 = -4.001952648

Simplifying
x + -0.125 = -4.001952648

Reorder the terms:
-0.125 + x = -4.001952648

Solving
-0.125 + x = -4.001952648

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 = -4.001952648 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + x = -4.001952648 + 0.125
x = -4.001952648 + 0.125

Combine like terms: -4.001952648 + 0.125 = -3.876952648
x = -3.876952648

Simplifying
x = -3.876952648


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.126952648, -3.876952648}

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