10-10*x-80*x^2=0

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Solution for 10-10*x-80*x^2=0 equation: 


Simplifying
10 + -10x + -80x2 = 0

Solving
10 + -10x + -80x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '10'.
10(1 + -1x + -8x2) = 0

Ignore the factor 10.

Subproblem 1
Set the factor '(1 + -1x + -8x2)' equal to zero and attempt to solve:

Simplifying
1 + -1x + -8x2 = 0

Solving
1 + -1x + -8x2 = 0

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
-0.125 + 0.125x + x2 = 0

Move the constant term to the right:

Add '0.125' to each side of the equation.
-0.125 + 0.125x + 0.125 + x2 = 0 + 0.125

Reorder the terms:
-0.125 + 0.125 + 0.125x + x2 = 0 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + 0.125x + x2 = 0 + 0.125
0.125x + x2 = 0 + 0.125

Combine like terms: 0 + 0.125 = 0.125
0.125x + x2 = 0.125

The x term is 0.125x.  Take half its coefficient (0.0625).
Square it (0.00390625) and add it to both sides.

Add '0.00390625' to each side of the equation.
0.125x + 0.00390625 + x2 = 0.125 + 0.00390625

Reorder the terms:
0.00390625 + 0.125x + x2 = 0.125 + 0.00390625

Combine like terms: 0.125 + 0.00390625 = 0.12890625
0.00390625 + 0.125x + x2 = 0.12890625

Factor a perfect square on the left side:
(x + 0.0625)(x + 0.0625) = 0.12890625

Calculate the square root of the right side: 0.359035165

Break this problem into two subproblems by setting 
(x + 0.0625) equal to 0.359035165 and -0.359035165.


Subproblem 1
x + 0.0625 = 0.359035165

Simplifying
x + 0.0625 = 0.359035165

Reorder the terms:
0.0625 + x = 0.359035165

Solving
0.0625 + x = 0.359035165

Solving for variable 'x'.

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

Add '-0.0625' to each side of the equation.
0.0625 + -0.0625 + x = 0.359035165 + -0.0625

Combine like terms: 0.0625 + -0.0625 = 0.0000
0.0000 + x = 0.359035165 + -0.0625
x = 0.359035165 + -0.0625

Combine like terms: 0.359035165 + -0.0625 = 0.296535165
x = 0.296535165

Simplifying
x = 0.296535165


Subproblem 2
x + 0.0625 = -0.359035165

Simplifying
x + 0.0625 = -0.359035165

Reorder the terms:
0.0625 + x = -0.359035165

Solving
0.0625 + x = -0.359035165

Solving for variable 'x'.

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

Add '-0.0625' to each side of the equation.
0.0625 + -0.0625 + x = -0.359035165 + -0.0625

Combine like terms: 0.0625 + -0.0625 = 0.0000
0.0000 + x = -0.359035165 + -0.0625
x = -0.359035165 + -0.0625

Combine like terms: -0.359035165 + -0.0625 = -0.421535165
x = -0.421535165

Simplifying
x = -0.421535165


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.296535165, -0.421535165}
Solution
x = {0.296535165, -0.421535165}

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