x*(x+0.25)=0.125

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Solution for x*(x+0.25)=0.125 equation: 


Simplifying
x(x + 0.25) = 0.125

Reorder the terms:
x(0.25 + x) = 0.125
(0.25 * x + x * x) = 0.125
(0.25x + x2) = 0.125

Solving
0.25x + x2 = 0.125

Solving for variable 'x'.

Reorder the terms:
-0.125 + 0.25x + x2 = 0.125 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
-0.125 + 0.25x + x2 = 0.000

Begin completing the square.

Move the constant term to the right:

Add '0.125' to each side of the equation.
-0.125 + 0.25x + 0.125 + x2 = 0.000 + 0.125

Reorder the terms:
-0.125 + 0.125 + 0.25x + x2 = 0.000 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + 0.25x + x2 = 0.000 + 0.125
0.25x + x2 = 0.000 + 0.125

Combine like terms: 0.000 + 0.125 = 0.125
0.25x + x2 = 0.125

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 = 0.125 + 0.015625

Reorder the terms:
0.015625 + 0.25x + x2 = 0.125 + 0.015625

Combine like terms: 0.125 + 0.015625 = 0.140625
0.015625 + 0.25x + x2 = 0.140625

Factor a perfect square on the left side:
(x + 0.125)(x + 0.125) = 0.140625

Calculate the square root of the right side: 0.375

Break this problem into two subproblems by setting 
(x + 0.125) equal to 0.375 and -0.375.


Subproblem 1
x + 0.125 = 0.375

Simplifying
x + 0.125 = 0.375

Reorder the terms:
0.125 + x = 0.375

Solving
0.125 + x = 0.375

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 = 0.375 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + x = 0.375 + -0.125
x = 0.375 + -0.125

Combine like terms: 0.375 + -0.125 = 0.25
x = 0.25

Simplifying
x = 0.25


Subproblem 2
x + 0.125 = -0.375

Simplifying
x + 0.125 = -0.375

Reorder the terms:
0.125 + x = -0.375

Solving
0.125 + x = -0.375

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 = -0.375 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + x = -0.375 + -0.125
x = -0.375 + -0.125

Combine like terms: -0.375 + -0.125 = -0.5
x = -0.5

Simplifying
x = -0.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.25, -0.5}

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