x^2=0.000103-0.00069x

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Solution for x^2=0.000103-0.00069x equation: 


Simplifying
x2 = 0.000103 + -0.00069x

Solving
x2 = 0.000103 + -0.00069x

Solving for variable 'x'.

Reorder the terms:
-0.000103 + 0.00069x + x2 = 0.000103 + -0.00069x + -0.000103 + 0.00069x

Reorder the terms:
-0.000103 + 0.00069x + x2 = 0.000103 + -0.000103 + -0.00069x + 0.00069x

Combine like terms: 0.000103 + -0.000103 = 0.000000
-0.000103 + 0.00069x + x2 = 0.000000 + -0.00069x + 0.00069x
-0.000103 + 0.00069x + x2 = -0.00069x + 0.00069x

Combine like terms: -0.00069x + 0.00069x = 0.00000
-0.000103 + 0.00069x + x2 = 0.00000

Begin completing the square.

Move the constant term to the right:

Add '0.000103' to each side of the equation.
-0.000103 + 0.00069x + 0.000103 + x2 = 0.00000 + 0.000103

Reorder the terms:
-0.000103 + 0.000103 + 0.00069x + x2 = 0.00000 + 0.000103

Combine like terms: -0.000103 + 0.000103 = 0.000000
0.000000 + 0.00069x + x2 = 0.00000 + 0.000103
0.00069x + x2 = 0.00000 + 0.000103

Combine like terms: 0.00000 + 0.000103 = 0.000103
0.00069x + x2 = 0.000103

The x term is 0.00069x.  Take half its coefficient (0.000345).
Square it (0.000000119025) and add it to both sides.

Add '0.000000119025' to each side of the equation.
0.00069x + 0.000000119025 + x2 = 0.000103 + 0.000000119025

Reorder the terms:
0.000000119025 + 0.00069x + x2 = 0.000103 + 0.000000119025

Combine like terms: 0.000103 + 0.000000119025 = 0.000103119025
0.000000119025 + 0.00069x + x2 = 0.000103119025

Factor a perfect square on the left side:
(x + 0.000345)(x + 0.000345) = 0.000103119025

Calculate the square root of the right side: 0.010154754

Break this problem into two subproblems by setting 
(x + 0.000345) equal to 0.010154754 and -0.010154754.


Subproblem 1
x + 0.000345 = 0.010154754

Simplifying
x + 0.000345 = 0.010154754

Reorder the terms:
0.000345 + x = 0.010154754

Solving
0.000345 + x = 0.010154754

Solving for variable 'x'.

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

Add '-0.000345' to each side of the equation.
0.000345 + -0.000345 + x = 0.010154754 + -0.000345

Combine like terms: 0.000345 + -0.000345 = 0.000000
0.000000 + x = 0.010154754 + -0.000345
x = 0.010154754 + -0.000345

Combine like terms: 0.010154754 + -0.000345 = 0.009809754
x = 0.009809754

Simplifying
x = 0.009809754


Subproblem 2
x + 0.000345 = -0.010154754

Simplifying
x + 0.000345 = -0.010154754

Reorder the terms:
0.000345 + x = -0.010154754

Solving
0.000345 + x = -0.010154754

Solving for variable 'x'.

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

Add '-0.000345' to each side of the equation.
0.000345 + -0.000345 + x = -0.010154754 + -0.000345

Combine like terms: 0.000345 + -0.000345 = 0.000000
0.000000 + x = -0.010154754 + -0.000345
x = -0.010154754 + -0.000345

Combine like terms: -0.010154754 + -0.000345 = -0.010499754
x = -0.010499754

Simplifying
x = -0.010499754


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.009809754, -0.010499754}

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