x^2=0.000317-0.00072x-0.00041x^2

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Solution for x^2=0.000317-0.00072x-0.00041x^2 equation: 


Simplifying
x2 = 0.000317 + -0.00072x + -0.00041x2

Solving
x2 = 0.000317 + -0.00072x + -0.00041x2

Solving for variable 'x'.

Reorder the terms:
-0.000317 + 0.00072x + x2 + 0.00041x2 = 0.000317 + -0.00072x + -0.00041x2 + -0.000317 + 0.00072x + 0.00041x2

Combine like terms: x2 + 0.00041x2 = 1.00041x2
-0.000317 + 0.00072x + 1.00041x2 = 0.000317 + -0.00072x + -0.00041x2 + -0.000317 + 0.00072x + 0.00041x2

Reorder the terms:
-0.000317 + 0.00072x + 1.00041x2 = 0.000317 + -0.000317 + -0.00072x + 0.00072x + -0.00041x2 + 0.00041x2

Combine like terms: 0.000317 + -0.000317 = 0.000000
-0.000317 + 0.00072x + 1.00041x2 = 0.000000 + -0.00072x + 0.00072x + -0.00041x2 + 0.00041x2
-0.000317 + 0.00072x + 1.00041x2 = -0.00072x + 0.00072x + -0.00041x2 + 0.00041x2

Combine like terms: -0.00072x + 0.00072x = 0.00000
-0.000317 + 0.00072x + 1.00041x2 = 0.00000 + -0.00041x2 + 0.00041x2
-0.000317 + 0.00072x + 1.00041x2 = -0.00041x2 + 0.00041x2

Combine like terms: -0.00041x2 + 0.00041x2 = 0.00000
-0.000317 + 0.00072x + 1.00041x2 = 0.00000

Begin completing the square.  Divide all terms by
1.00041 the coefficient of the squared term: 

Divide each side by '1.00041'.
-0.0003168700833 + 0.000719704921x + x2 = 0

Move the constant term to the right:

Add '0.0003168700833' to each side of the equation.
-0.0003168700833 + 0.000719704921x + 0.0003168700833 + x2 = 0 + 0.0003168700833

Reorder the terms:
-0.0003168700833 + 0.0003168700833 + 0.000719704921x + x2 = 0 + 0.0003168700833

Combine like terms: -0.0003168700833 + 0.0003168700833 = 0.0000000000000
0.0000000000000 + 0.000719704921x + x2 = 0 + 0.0003168700833
0.000719704921x + x2 = 0 + 0.0003168700833

Combine like terms: 0 + 0.0003168700833 = 0.0003168700833
0.000719704921x + x2 = 0.0003168700833

The x term is 0.000719704921x.  Take half its coefficient (0.0003598524605).
Square it (0.0000001294937933) and add it to both sides.

Add '0.0000001294937933' to each side of the equation.
0.000719704921x + 0.0000001294937933 + x2 = 0.0003168700833 + 0.0000001294937933

Reorder the terms:
0.0000001294937933 + 0.000719704921x + x2 = 0.0003168700833 + 0.0000001294937933

Combine like terms: 0.0003168700833 + 0.0000001294937933 = 0.0003169995770933
0.0000001294937933 + 0.000719704921x + x2 = 0.0003169995770933

Factor a perfect square on the left side:
(x + 0.0003598524605)(x + 0.0003598524605) = 0.0003169995770933

Calculate the square root of the right side: 0.017804482

Break this problem into two subproblems by setting 
(x + 0.0003598524605) equal to 0.017804482 and -0.017804482.


Subproblem 1
x + 0.0003598524605 = 0.017804482

Simplifying
x + 0.0003598524605 = 0.017804482

Reorder the terms:
0.0003598524605 + x = 0.017804482

Solving
0.0003598524605 + x = 0.017804482

Solving for variable 'x'.

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

Add '-0.0003598524605' to each side of the equation.
0.0003598524605 + -0.0003598524605 + x = 0.017804482 + -0.0003598524605

Combine like terms: 0.0003598524605 + -0.0003598524605 = 0.0000000000000
0.0000000000000 + x = 0.017804482 + -0.0003598524605
x = 0.017804482 + -0.0003598524605

Combine like terms: 0.017804482 + -0.0003598524605 = 0.0174446295395
x = 0.0174446295395

Simplifying
x = 0.0174446295395


Subproblem 2
x + 0.0003598524605 = -0.017804482

Simplifying
x + 0.0003598524605 = -0.017804482

Reorder the terms:
0.0003598524605 + x = -0.017804482

Solving
0.0003598524605 + x = -0.017804482

Solving for variable 'x'.

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

Add '-0.0003598524605' to each side of the equation.
0.0003598524605 + -0.0003598524605 + x = -0.017804482 + -0.0003598524605

Combine like terms: 0.0003598524605 + -0.0003598524605 = 0.0000000000000
0.0000000000000 + x = -0.017804482 + -0.0003598524605
x = -0.017804482 + -0.0003598524605

Combine like terms: -0.017804482 + -0.0003598524605 = -0.0181643344605
x = -0.0181643344605

Simplifying
x = -0.0181643344605


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.0174446295395, -0.0181643344605}

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