0.75(0.125-x)-4x^2=0

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Solution for 0.75(0.125-x)-4x^2=0 equation: 


Simplifying
0.75(0.125 + -1x) + -4x2 = 0
(0.125 * 0.75 + -1x * 0.75) + -4x2 = 0
(0.09375 + -0.75x) + -4x2 = 0

Solving
0.09375 + -0.75x + -4x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-0.0234375 + 0.1875x + x2 = 0

Move the constant term to the right:

Add '0.0234375' to each side of the equation.
-0.0234375 + 0.1875x + 0.0234375 + x2 = 0 + 0.0234375

Reorder the terms:
-0.0234375 + 0.0234375 + 0.1875x + x2 = 0 + 0.0234375

Combine like terms: -0.0234375 + 0.0234375 = 0.0000000
0.0000000 + 0.1875x + x2 = 0 + 0.0234375
0.1875x + x2 = 0 + 0.0234375

Combine like terms: 0 + 0.0234375 = 0.0234375
0.1875x + x2 = 0.0234375

The x term is 0.1875x.  Take half its coefficient (0.09375).
Square it (0.0087890625) and add it to both sides.

Add '0.0087890625' to each side of the equation.
0.1875x + 0.0087890625 + x2 = 0.0234375 + 0.0087890625

Reorder the terms:
0.0087890625 + 0.1875x + x2 = 0.0234375 + 0.0087890625

Combine like terms: 0.0234375 + 0.0087890625 = 0.0322265625
0.0087890625 + 0.1875x + x2 = 0.0322265625

Factor a perfect square on the left side:
(x + 0.09375)(x + 0.09375) = 0.0322265625

Calculate the square root of the right side: 0.179517583

Break this problem into two subproblems by setting 
(x + 0.09375) equal to 0.179517583 and -0.179517583.


Subproblem 1
x + 0.09375 = 0.179517583

Simplifying
x + 0.09375 = 0.179517583

Reorder the terms:
0.09375 + x = 0.179517583

Solving
0.09375 + x = 0.179517583

Solving for variable 'x'.

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

Add '-0.09375' to each side of the equation.
0.09375 + -0.09375 + x = 0.179517583 + -0.09375

Combine like terms: 0.09375 + -0.09375 = 0.00000
0.00000 + x = 0.179517583 + -0.09375
x = 0.179517583 + -0.09375

Combine like terms: 0.179517583 + -0.09375 = 0.085767583
x = 0.085767583

Simplifying
x = 0.085767583


Subproblem 2
x + 0.09375 = -0.179517583

Simplifying
x + 0.09375 = -0.179517583

Reorder the terms:
0.09375 + x = -0.179517583

Solving
0.09375 + x = -0.179517583

Solving for variable 'x'.

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

Add '-0.09375' to each side of the equation.
0.09375 + -0.09375 + x = -0.179517583 + -0.09375

Combine like terms: 0.09375 + -0.09375 = 0.00000
0.00000 + x = -0.179517583 + -0.09375
x = -0.179517583 + -0.09375

Combine like terms: -0.179517583 + -0.09375 = -0.273267583
x = -0.273267583

Simplifying
x = -0.273267583


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.085767583, -0.273267583}

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