x^2+0.25x-0.065=0

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Solution for x^2+0.25x-0.065=0 equation: 


Simplifying
x2 + 0.25x + -0.065 = 0

Reorder the terms:
-0.065 + 0.25x + x2 = 0

Solving
-0.065 + 0.25x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '0.065' to each side of the equation.
-0.065 + 0.25x + 0.065 + x2 = 0 + 0.065

Reorder the terms:
-0.065 + 0.065 + 0.25x + x2 = 0 + 0.065

Combine like terms: -0.065 + 0.065 = 0.000
0.000 + 0.25x + x2 = 0 + 0.065
0.25x + x2 = 0 + 0.065

Combine like terms: 0 + 0.065 = 0.065
0.25x + x2 = 0.065

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 = 0.065 + 0.015625

Reorder the terms:
0.015625 + 0.25x + x2 = 0.065 + 0.015625

Combine like terms: 0.065 + 0.015625 = 0.080625
0.015625 + 0.25x + x2 = 0.080625

Factor a perfect square on the left side:
(x + 0.125)(x + 0.125) = 0.080625

Calculate the square root of the right side: 0.283945417

Break this problem into two subproblems by setting 
(x + 0.125) equal to 0.283945417 and -0.283945417.


Subproblem 1
x + 0.125 = 0.283945417

Simplifying
x + 0.125 = 0.283945417

Reorder the terms:
0.125 + x = 0.283945417

Solving
0.125 + x = 0.283945417

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 = 0.283945417 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + x = 0.283945417 + -0.125
x = 0.283945417 + -0.125

Combine like terms: 0.283945417 + -0.125 = 0.158945417
x = 0.158945417

Simplifying
x = 0.158945417


Subproblem 2
x + 0.125 = -0.283945417

Simplifying
x + 0.125 = -0.283945417

Reorder the terms:
0.125 + x = -0.283945417

Solving
0.125 + x = -0.283945417

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 = -0.283945417 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + x = -0.283945417 + -0.125
x = -0.283945417 + -0.125

Combine like terms: -0.283945417 + -0.125 = -0.408945417
x = -0.408945417

Simplifying
x = -0.408945417


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.158945417, -0.408945417}

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