X^2+0.25*X-0.0625=0

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Solution for X^2+0.25*X-0.0625=0 equation: 


Simplifying
X2 + 0.25X + -0.0625 = 0

Reorder the terms:
-0.0625 + 0.25X + X2 = 0

Solving
-0.0625 + 0.25X + X2 = 0

Solving for variable 'X'.

Begin completing the square.

Move the constant term to the right:

Add '0.0625' to each side of the equation.
-0.0625 + 0.25X + 0.0625 + X2 = 0 + 0.0625

Reorder the terms:
-0.0625 + 0.0625 + 0.25X + X2 = 0 + 0.0625

Combine like terms: -0.0625 + 0.0625 = 0.0000
0.0000 + 0.25X + X2 = 0 + 0.0625
0.25X + X2 = 0 + 0.0625

Combine like terms: 0 + 0.0625 = 0.0625
0.25X + X2 = 0.0625

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 = 0.0625 + 0.015625

Reorder the terms:
0.015625 + 0.25X + X2 = 0.0625 + 0.015625

Combine like terms: 0.0625 + 0.015625 = 0.078125
0.015625 + 0.25X + X2 = 0.078125

Factor a perfect square on the left side:
(X + 0.125)(X + 0.125) = 0.078125

Calculate the square root of the right side: 0.279508497

Break this problem into two subproblems by setting 
(X + 0.125) equal to 0.279508497 and -0.279508497.


Subproblem 1
X + 0.125 = 0.279508497

Simplifying
X + 0.125 = 0.279508497

Reorder the terms:
0.125 + X = 0.279508497

Solving
0.125 + X = 0.279508497

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 = 0.279508497 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + X = 0.279508497 + -0.125
X = 0.279508497 + -0.125

Combine like terms: 0.279508497 + -0.125 = 0.154508497
X = 0.154508497

Simplifying
X = 0.154508497


Subproblem 2
X + 0.125 = -0.279508497

Simplifying
X + 0.125 = -0.279508497

Reorder the terms:
0.125 + X = -0.279508497

Solving
0.125 + X = -0.279508497

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 = -0.279508497 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + X = -0.279508497 + -0.125
X = -0.279508497 + -0.125

Combine like terms: -0.279508497 + -0.125 = -0.404508497
X = -0.404508497

Simplifying
X = -0.404508497


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {0.154508497, -0.404508497}

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