x^2-8.1616161616x-7.5=0

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Solution for x^2-8.1616161616x-7.5=0 equation: 


Simplifying
x2 + -8.1616161616x + -7.5 = 0

Reorder the terms:
-7.5 + -8.1616161616x + x2 = 0

Solving
-7.5 + -8.1616161616x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '7.5' to each side of the equation.
-7.5 + -8.1616161616x + 7.5 + x2 = 0 + 7.5

Reorder the terms:
-7.5 + 7.5 + -8.1616161616x + x2 = 0 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + -8.1616161616x + x2 = 0 + 7.5
-8.1616161616x + x2 = 0 + 7.5

Combine like terms: 0 + 7.5 = 7.5
-8.1616161616x + x2 = 7.5

The x term is -8.1616161616x.  Take half its coefficient (-4.080808081).
Square it (16.65299459) and add it to both sides.

Add '16.65299459' to each side of the equation.
-8.1616161616x + 16.65299459 + x2 = 7.5 + 16.65299459

Reorder the terms:
16.65299459 + -8.1616161616x + x2 = 7.5 + 16.65299459

Combine like terms: 7.5 + 16.65299459 = 24.15299459
16.65299459 + -8.1616161616x + x2 = 24.15299459

Factor a perfect square on the left side:
(x + -4.080808081)(x + -4.080808081) = 24.15299459

Calculate the square root of the right side: 4.914569624

Break this problem into two subproblems by setting 
(x + -4.080808081) equal to 4.914569624 and -4.914569624.


Subproblem 1
x + -4.080808081 = 4.914569624

Simplifying
x + -4.080808081 = 4.914569624

Reorder the terms:
-4.080808081 + x = 4.914569624

Solving
-4.080808081 + x = 4.914569624

Solving for variable 'x'.

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

Add '4.080808081' to each side of the equation.
-4.080808081 + 4.080808081 + x = 4.914569624 + 4.080808081

Combine like terms: -4.080808081 + 4.080808081 = 0.000000000
0.000000000 + x = 4.914569624 + 4.080808081
x = 4.914569624 + 4.080808081

Combine like terms: 4.914569624 + 4.080808081 = 8.995377705
x = 8.995377705

Simplifying
x = 8.995377705


Subproblem 2
x + -4.080808081 = -4.914569624

Simplifying
x + -4.080808081 = -4.914569624

Reorder the terms:
-4.080808081 + x = -4.914569624

Solving
-4.080808081 + x = -4.914569624

Solving for variable 'x'.

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

Add '4.080808081' to each side of the equation.
-4.080808081 + 4.080808081 + x = -4.914569624 + 4.080808081

Combine like terms: -4.080808081 + 4.080808081 = 0.000000000
0.000000000 + x = -4.914569624 + 4.080808081
x = -4.914569624 + 4.080808081

Combine like terms: -4.914569624 + 4.080808081 = -0.833761543
x = -0.833761543

Simplifying
x = -0.833761543


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.995377705, -0.833761543}

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