0.000068-0.0068x-x^2=0

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Solution for 0.000068-0.0068x-x^2=0 equation: 


Simplifying
0.000068 + -0.0068x + -1x2 = 0

Solving
0.000068 + -0.0068x + -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'.
-0.000068 + 0.0068x + x2 = 0

Move the constant term to the right:

Add '0.000068' to each side of the equation.
-0.000068 + 0.0068x + 0.000068 + x2 = 0 + 0.000068

Reorder the terms:
-0.000068 + 0.000068 + 0.0068x + x2 = 0 + 0.000068

Combine like terms: -0.000068 + 0.000068 = 0.000000
0.000000 + 0.0068x + x2 = 0 + 0.000068
0.0068x + x2 = 0 + 0.000068

Combine like terms: 0 + 0.000068 = 0.000068
0.0068x + x2 = 0.000068

The x term is 0.0068x.  Take half its coefficient (0.0034).
Square it (0.00001156) and add it to both sides.

Add '0.00001156' to each side of the equation.
0.0068x + 0.00001156 + x2 = 0.000068 + 0.00001156

Reorder the terms:
0.00001156 + 0.0068x + x2 = 0.000068 + 0.00001156

Combine like terms: 0.000068 + 0.00001156 = 0.00007956
0.00001156 + 0.0068x + x2 = 0.00007956

Factor a perfect square on the left side:
(x + 0.0034)(x + 0.0034) = 0.00007956

Calculate the square root of the right side: 0.008919641

Break this problem into two subproblems by setting 
(x + 0.0034) equal to 0.008919641 and -0.008919641.


Subproblem 1
x + 0.0034 = 0.008919641

Simplifying
x + 0.0034 = 0.008919641

Reorder the terms:
0.0034 + x = 0.008919641

Solving
0.0034 + x = 0.008919641

Solving for variable 'x'.

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

Add '-0.0034' to each side of the equation.
0.0034 + -0.0034 + x = 0.008919641 + -0.0034

Combine like terms: 0.0034 + -0.0034 = 0.0000
0.0000 + x = 0.008919641 + -0.0034
x = 0.008919641 + -0.0034

Combine like terms: 0.008919641 + -0.0034 = 0.005519641
x = 0.005519641

Simplifying
x = 0.005519641


Subproblem 2
x + 0.0034 = -0.008919641

Simplifying
x + 0.0034 = -0.008919641

Reorder the terms:
0.0034 + x = -0.008919641

Solving
0.0034 + x = -0.008919641

Solving for variable 'x'.

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

Add '-0.0034' to each side of the equation.
0.0034 + -0.0034 + x = -0.008919641 + -0.0034

Combine like terms: 0.0034 + -0.0034 = 0.0000
0.0000 + x = -0.008919641 + -0.0034
x = -0.008919641 + -0.0034

Combine like terms: -0.008919641 + -0.0034 = -0.012319641
x = -0.012319641

Simplifying
x = -0.012319641


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.005519641, -0.012319641}

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