0.0000068-0.00068x-x^2=

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Solution for 0.0000068-0.00068x-x^2= equation:


Simplifying
0.0000068 + -0.00068x + -1x2 = 0

Solving
0.0000068 + -0.00068x + -1x2 = 0

Solving for variable 'x'.

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

Divide each side by '-1'.
-0.0000068 + 0.00068x + x2 = 0

Move the constant term to the right:

Add '0.0000068' to each side of the equation.
-0.0000068 + 0.00068x + 0.0000068 + x2 = 0 + 0.0000068

Reorder the terms:
-0.0000068 + 0.0000068 + 0.00068x + x2 = 0 + 0.0000068

Combine like terms: -0.0000068 + 0.0000068 = 0.0000000
0.0000000 + 0.00068x + x2 = 0 + 0.0000068
0.00068x + x2 = 0 + 0.0000068

Combine like terms: 0 + 0.0000068 = 0.0000068
0.00068x + x2 = 0.0000068

The x term is 0.00068x.  Take half its coefficient (0.00034).
Square it (0.0000001156) and add it to both sides.

Add '0.0000001156' to each side of the equation.
0.00068x + 0.0000001156 + x2 = 0.0000068 + 0.0000001156

Reorder the terms:
0.0000001156 + 0.00068x + x2 = 0.0000068 + 0.0000001156

Combine like terms: 0.0000068 + 0.0000001156 = 0.0000069156
0.0000001156 + 0.00068x + x2 = 0.0000069156

Factor a perfect square on the left side:
(x + 0.00034)(x + 0.00034) = 0.0000069156

Calculate the square root of the right side: 0.002629753

Break this problem into two subproblems by setting 
(x + 0.00034) equal to 0.002629753 and -0.002629753.


Subproblem 1
x + 0.00034 = 0.002629753

Simplifying
x + 0.00034 = 0.002629753

Reorder the terms:
0.00034 + x = 0.002629753

Solving
0.00034 + x = 0.002629753

Solving for variable 'x'.

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

Add '-0.00034' to each side of the equation.
0.00034 + -0.00034 + x = 0.002629753 + -0.00034

Combine like terms: 0.00034 + -0.00034 = 0.00000
0.00000 + x = 0.002629753 + -0.00034
x = 0.002629753 + -0.00034

Combine like terms: 0.002629753 + -0.00034 = 0.002289753
x = 0.002289753

Simplifying
x = 0.002289753


Subproblem 2
x + 0.00034 = -0.002629753

Simplifying
x + 0.00034 = -0.002629753

Reorder the terms:
0.00034 + x = -0.002629753

Solving
0.00034 + x = -0.002629753

Solving for variable 'x'.

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

Add '-0.00034' to each side of the equation.
0.00034 + -0.00034 + x = -0.002629753 + -0.00034

Combine like terms: 0.00034 + -0.00034 = 0.00000
0.00000 + x = -0.002629753 + -0.00034
x = -0.002629753 + -0.00034

Combine like terms: -0.002629753 + -0.00034 = -0.002969753
x = -0.002969753

Simplifying
x = -0.002969753


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.002289753, -0.002969753}

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