x(x+0.0075)=0.000225

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Solution for x(x+0.0075)=0.000225 equation: 


Simplifying
x(x + 0.0075) = 0.000225

Reorder the terms:
x(0.0075 + x) = 0.000225
(0.0075 * x + x * x) = 0.000225
(0.0075x + x2) = 0.000225

Solving
0.0075x + x2 = 0.000225

Solving for variable 'x'.

Reorder the terms:
-0.000225 + 0.0075x + x2 = 0.000225 + -0.000225

Combine like terms: 0.000225 + -0.000225 = 0.000000
-0.000225 + 0.0075x + x2 = 0.000000

Begin completing the square.

Move the constant term to the right:

Add '0.000225' to each side of the equation.
-0.000225 + 0.0075x + 0.000225 + x2 = 0.000000 + 0.000225

Reorder the terms:
-0.000225 + 0.000225 + 0.0075x + x2 = 0.000000 + 0.000225

Combine like terms: -0.000225 + 0.000225 = 0.000000
0.000000 + 0.0075x + x2 = 0.000000 + 0.000225
0.0075x + x2 = 0.000000 + 0.000225

Combine like terms: 0.000000 + 0.000225 = 0.000225
0.0075x + x2 = 0.000225

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 = 0.000225 + 0.0000140625

Reorder the terms:
0.0000140625 + 0.0075x + x2 = 0.000225 + 0.0000140625

Combine like terms: 0.000225 + 0.0000140625 = 0.0002390625
0.0000140625 + 0.0075x + x2 = 0.0002390625

Factor a perfect square on the left side:
(x + 0.00375)(x + 0.00375) = 0.0002390625

Calculate the square root of the right side: 0.015461646

Break this problem into two subproblems by setting 
(x + 0.00375) equal to 0.015461646 and -0.015461646.


Subproblem 1
x + 0.00375 = 0.015461646

Simplifying
x + 0.00375 = 0.015461646

Reorder the terms:
0.00375 + x = 0.015461646

Solving
0.00375 + x = 0.015461646

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 = 0.015461646 + -0.00375

Combine like terms: 0.00375 + -0.00375 = 0.00000
0.00000 + x = 0.015461646 + -0.00375
x = 0.015461646 + -0.00375

Combine like terms: 0.015461646 + -0.00375 = 0.011711646
x = 0.011711646

Simplifying
x = 0.011711646


Subproblem 2
x + 0.00375 = -0.015461646

Simplifying
x + 0.00375 = -0.015461646

Reorder the terms:
0.00375 + x = -0.015461646

Solving
0.00375 + x = -0.015461646

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 = -0.015461646 + -0.00375

Combine like terms: 0.00375 + -0.00375 = 0.00000
0.00000 + x = -0.015461646 + -0.00375
x = -0.015461646 + -0.00375

Combine like terms: -0.015461646 + -0.00375 = -0.019211646
x = -0.019211646

Simplifying
x = -0.019211646


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.011711646, -0.019211646}

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