x(x+0.0075)=0.00075

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Solution for x(x+0.0075)=0.00075 equation: 


Simplifying
x(x + 0.0075) = 0.00075

Reorder the terms:
x(0.0075 + x) = 0.00075
(0.0075 * x + x * x) = 0.00075
(0.0075x + x2) = 0.00075

Solving
0.0075x + x2 = 0.00075

Solving for variable 'x'.

Reorder the terms:
-0.00075 + 0.0075x + x2 = 0.00075 + -0.00075

Combine like terms: 0.00075 + -0.00075 = 0.00000
-0.00075 + 0.0075x + x2 = 0.00000

Begin completing the square.

Move the constant term to the right:

Add '0.00075' to each side of the equation.
-0.00075 + 0.0075x + 0.00075 + x2 = 0.00000 + 0.00075

Reorder the terms:
-0.00075 + 0.00075 + 0.0075x + x2 = 0.00000 + 0.00075

Combine like terms: -0.00075 + 0.00075 = 0.00000
0.00000 + 0.0075x + x2 = 0.00000 + 0.00075
0.0075x + x2 = 0.00000 + 0.00075

Combine like terms: 0.00000 + 0.00075 = 0.00075
0.0075x + x2 = 0.00075

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 = 0.00075 + 0.0000140625

Reorder the terms:
0.0000140625 + 0.0075x + x2 = 0.00075 + 0.0000140625

Combine like terms: 0.00075 + 0.0000140625 = 0.0007640625
0.0000140625 + 0.0075x + x2 = 0.0007640625

Factor a perfect square on the left side:
(x + 0.00375)(x + 0.00375) = 0.0007640625

Calculate the square root of the right side: 0.02764168

Break this problem into two subproblems by setting 
(x + 0.00375) equal to 0.02764168 and -0.02764168.


Subproblem 1
x + 0.00375 = 0.02764168

Simplifying
x + 0.00375 = 0.02764168

Reorder the terms:
0.00375 + x = 0.02764168

Solving
0.00375 + x = 0.02764168

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 = 0.02764168 + -0.00375

Combine like terms: 0.00375 + -0.00375 = 0.00000
0.00000 + x = 0.02764168 + -0.00375
x = 0.02764168 + -0.00375

Combine like terms: 0.02764168 + -0.00375 = 0.02389168
x = 0.02389168

Simplifying
x = 0.02389168


Subproblem 2
x + 0.00375 = -0.02764168

Simplifying
x + 0.00375 = -0.02764168

Reorder the terms:
0.00375 + x = -0.02764168

Solving
0.00375 + x = -0.02764168

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 = -0.02764168 + -0.00375

Combine like terms: 0.00375 + -0.00375 = 0.00000
0.00000 + x = -0.02764168 + -0.00375
x = -0.02764168 + -0.00375

Combine like terms: -0.02764168 + -0.00375 = -0.03139168
x = -0.03139168

Simplifying
x = -0.03139168


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.02389168, -0.03139168}

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