7x^2-4x-4=0

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Solution for 7x^2-4x-4=0 equation: 


Simplifying
7x2 + -4x + -4 = 0

Reorder the terms:
-4 + -4x + 7x2 = 0

Solving
-4 + -4x + 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'.
-0.5714285714 + -0.5714285714x + x2 = 0

Move the constant term to the right:

Add '0.5714285714' to each side of the equation.
-0.5714285714 + -0.5714285714x + 0.5714285714 + x2 = 0 + 0.5714285714

Reorder the terms:
-0.5714285714 + 0.5714285714 + -0.5714285714x + x2 = 0 + 0.5714285714

Combine like terms: -0.5714285714 + 0.5714285714 = 0.0000000000
0.0000000000 + -0.5714285714x + x2 = 0 + 0.5714285714
-0.5714285714x + x2 = 0 + 0.5714285714

Combine like terms: 0 + 0.5714285714 = 0.5714285714
-0.5714285714x + x2 = 0.5714285714

The x term is -0.5714285714x.  Take half its coefficient (-0.2857142857).
Square it (0.08163265305) and add it to both sides.

Add '0.08163265305' to each side of the equation.
-0.5714285714x + 0.08163265305 + x2 = 0.5714285714 + 0.08163265305

Reorder the terms:
0.08163265305 + -0.5714285714x + x2 = 0.5714285714 + 0.08163265305

Combine like terms: 0.5714285714 + 0.08163265305 = 0.65306122445
0.08163265305 + -0.5714285714x + x2 = 0.65306122445

Factor a perfect square on the left side:
(x + -0.2857142857)(x + -0.2857142857) = 0.65306122445

Calculate the square root of the right side: 0.808122036

Break this problem into two subproblems by setting 
(x + -0.2857142857) equal to 0.808122036 and -0.808122036.


Subproblem 1
x + -0.2857142857 = 0.808122036

Simplifying
x + -0.2857142857 = 0.808122036

Reorder the terms:
-0.2857142857 + x = 0.808122036

Solving
-0.2857142857 + x = 0.808122036

Solving for variable 'x'.

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

Add '0.2857142857' to each side of the equation.
-0.2857142857 + 0.2857142857 + x = 0.808122036 + 0.2857142857

Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000
0.0000000000 + x = 0.808122036 + 0.2857142857
x = 0.808122036 + 0.2857142857

Combine like terms: 0.808122036 + 0.2857142857 = 1.0938363217
x = 1.0938363217

Simplifying
x = 1.0938363217


Subproblem 2
x + -0.2857142857 = -0.808122036

Simplifying
x + -0.2857142857 = -0.808122036

Reorder the terms:
-0.2857142857 + x = -0.808122036

Solving
-0.2857142857 + x = -0.808122036

Solving for variable 'x'.

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

Add '0.2857142857' to each side of the equation.
-0.2857142857 + 0.2857142857 + x = -0.808122036 + 0.2857142857

Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000
0.0000000000 + x = -0.808122036 + 0.2857142857
x = -0.808122036 + 0.2857142857

Combine like terms: -0.808122036 + 0.2857142857 = -0.5224077503
x = -0.5224077503

Simplifying
x = -0.5224077503


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.0938363217, -0.5224077503}

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