0.0075(0.05-x)=x*x

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Solution for 0.0075(0.05-x)=x*x equation: 


Simplifying
0.0075(0.05 + -1x) = x * x
(0.05 * 0.0075 + -1x * 0.0075) = x * x
(0.000375 + -0.0075x) = x * x

Multiply x * x
0.000375 + -0.0075x = x2

Solving
0.000375 + -0.0075x = x2

Solving for variable 'x'.

Combine like terms: x2 + -1x2 = 0
0.000375 + -0.0075x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-0.000375 + 0.0075x + x2 = 0

Move the constant term to the right:

Add '0.000375' to each side of the equation.
-0.000375 + 0.0075x + 0.000375 + x2 = 0 + 0.000375

Reorder the terms:
-0.000375 + 0.000375 + 0.0075x + x2 = 0 + 0.000375

Combine like terms: -0.000375 + 0.000375 = 0.000000
0.000000 + 0.0075x + x2 = 0 + 0.000375
0.0075x + x2 = 0 + 0.000375

Combine like terms: 0 + 0.000375 = 0.000375
0.0075x + x2 = 0.000375

The x term is 0.0075x.  Take half its coefficient (0.00375).
Square it (0.0000140625) and add it to both sides.

Add '0.0000140625' to each side of the equation.
0.0075x + 0.0000140625 + x2 = 0.000375 + 0.0000140625

Reorder the terms:
0.0000140625 + 0.0075x + x2 = 0.000375 + 0.0000140625

Combine like terms: 0.000375 + 0.0000140625 = 0.0003890625
0.0000140625 + 0.0075x + x2 = 0.0003890625

Factor a perfect square on the left side:
(x + 0.00375)(x + 0.00375) = 0.0003890625

Calculate the square root of the right side: 0.019724667

Break this problem into two subproblems by setting 
(x + 0.00375) equal to 0.019724667 and -0.019724667.


Subproblem 1
x + 0.00375 = 0.019724667

Simplifying
x + 0.00375 = 0.019724667

Reorder the terms:
0.00375 + x = 0.019724667

Solving
0.00375 + x = 0.019724667

Solving for variable 'x'.

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

Add '-0.00375' to each side of the equation.
0.00375 + -0.00375 + x = 0.019724667 + -0.00375

Combine like terms: 0.00375 + -0.00375 = 0.00000
0.00000 + x = 0.019724667 + -0.00375
x = 0.019724667 + -0.00375

Combine like terms: 0.019724667 + -0.00375 = 0.015974667
x = 0.015974667

Simplifying
x = 0.015974667


Subproblem 2
x + 0.00375 = -0.019724667

Simplifying
x + 0.00375 = -0.019724667

Reorder the terms:
0.00375 + x = -0.019724667

Solving
0.00375 + x = -0.019724667

Solving for variable 'x'.

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

Add '-0.00375' to each side of the equation.
0.00375 + -0.00375 + x = -0.019724667 + -0.00375

Combine like terms: 0.00375 + -0.00375 = 0.00000
0.00000 + x = -0.019724667 + -0.00375
x = -0.019724667 + -0.00375

Combine like terms: -0.019724667 + -0.00375 = -0.023474667
x = -0.023474667

Simplifying
x = -0.023474667


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.015974667, -0.023474667}

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