7x^2-6x-6=0

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Solution for 7x^2-6x-6=0 equation: 


Simplifying
7x2 + -6x + -6 = 0

Reorder the terms:
-6 + -6x + 7x2 = 0

Solving
-6 + -6x + 7x2 = 0

Solving for variable 'x'.

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

Divide each side by '7'.
-0.8571428571 + -0.8571428571x + x2 = 0

Move the constant term to the right:

Add '0.8571428571' to each side of the equation.
-0.8571428571 + -0.8571428571x + 0.8571428571 + x2 = 0 + 0.8571428571

Reorder the terms:
-0.8571428571 + 0.8571428571 + -0.8571428571x + x2 = 0 + 0.8571428571

Combine like terms: -0.8571428571 + 0.8571428571 = 0.0000000000
0.0000000000 + -0.8571428571x + x2 = 0 + 0.8571428571
-0.8571428571x + x2 = 0 + 0.8571428571

Combine like terms: 0 + 0.8571428571 = 0.8571428571
-0.8571428571x + x2 = 0.8571428571

The x term is -0.8571428571x.  Take half its coefficient (-0.4285714286).
Square it (0.1836734694) and add it to both sides.

Add '0.1836734694' to each side of the equation.
-0.8571428571x + 0.1836734694 + x2 = 0.8571428571 + 0.1836734694

Reorder the terms:
0.1836734694 + -0.8571428571x + x2 = 0.8571428571 + 0.1836734694

Combine like terms: 0.8571428571 + 0.1836734694 = 1.0408163265
0.1836734694 + -0.8571428571x + x2 = 1.0408163265

Factor a perfect square on the left side:
(x + -0.4285714286)(x + -0.4285714286) = 1.0408163265

Calculate the square root of the right side: 1.020204061

Break this problem into two subproblems by setting 
(x + -0.4285714286) equal to 1.020204061 and -1.020204061.


Subproblem 1
x + -0.4285714286 = 1.020204061

Simplifying
x + -0.4285714286 = 1.020204061

Reorder the terms:
-0.4285714286 + x = 1.020204061

Solving
-0.4285714286 + x = 1.020204061

Solving for variable 'x'.

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

Add '0.4285714286' to each side of the equation.
-0.4285714286 + 0.4285714286 + x = 1.020204061 + 0.4285714286

Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000
0.0000000000 + x = 1.020204061 + 0.4285714286
x = 1.020204061 + 0.4285714286

Combine like terms: 1.020204061 + 0.4285714286 = 1.4487754896
x = 1.4487754896

Simplifying
x = 1.4487754896


Subproblem 2
x + -0.4285714286 = -1.020204061

Simplifying
x + -0.4285714286 = -1.020204061

Reorder the terms:
-0.4285714286 + x = -1.020204061

Solving
-0.4285714286 + x = -1.020204061

Solving for variable 'x'.

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

Add '0.4285714286' to each side of the equation.
-0.4285714286 + 0.4285714286 + x = -1.020204061 + 0.4285714286

Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000
0.0000000000 + x = -1.020204061 + 0.4285714286
x = -1.020204061 + 0.4285714286

Combine like terms: -1.020204061 + 0.4285714286 = -0.5916326324
x = -0.5916326324

Simplifying
x = -0.5916326324


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.4487754896, -0.5916326324}

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