x^2+6.625x-6.625=0

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Solution for x^2+6.625x-6.625=0 equation: 


Simplifying
x2 + 6.625x + -6.625 = 0

Reorder the terms:
-6.625 + 6.625x + x2 = 0

Solving
-6.625 + 6.625x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '6.625' to each side of the equation.
-6.625 + 6.625x + 6.625 + x2 = 0 + 6.625

Reorder the terms:
-6.625 + 6.625 + 6.625x + x2 = 0 + 6.625

Combine like terms: -6.625 + 6.625 = 0.000
0.000 + 6.625x + x2 = 0 + 6.625
6.625x + x2 = 0 + 6.625

Combine like terms: 0 + 6.625 = 6.625
6.625x + x2 = 6.625

The x term is 6.625x.  Take half its coefficient (3.3125).
Square it (10.97265625) and add it to both sides.

Add '10.97265625' to each side of the equation.
6.625x + 10.97265625 + x2 = 6.625 + 10.97265625

Reorder the terms:
10.97265625 + 6.625x + x2 = 6.625 + 10.97265625

Combine like terms: 6.625 + 10.97265625 = 17.59765625
10.97265625 + 6.625x + x2 = 17.59765625

Factor a perfect square on the left side:
(x + 3.3125)(x + 3.3125) = 17.59765625

Calculate the square root of the right side: 4.194956049

Break this problem into two subproblems by setting 
(x + 3.3125) equal to 4.194956049 and -4.194956049.


Subproblem 1
x + 3.3125 = 4.194956049

Simplifying
x + 3.3125 = 4.194956049

Reorder the terms:
3.3125 + x = 4.194956049

Solving
3.3125 + x = 4.194956049

Solving for variable 'x'.

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

Add '-3.3125' to each side of the equation.
3.3125 + -3.3125 + x = 4.194956049 + -3.3125

Combine like terms: 3.3125 + -3.3125 = 0.0000
0.0000 + x = 4.194956049 + -3.3125
x = 4.194956049 + -3.3125

Combine like terms: 4.194956049 + -3.3125 = 0.882456049
x = 0.882456049

Simplifying
x = 0.882456049


Subproblem 2
x + 3.3125 = -4.194956049

Simplifying
x + 3.3125 = -4.194956049

Reorder the terms:
3.3125 + x = -4.194956049

Solving
3.3125 + x = -4.194956049

Solving for variable 'x'.

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

Add '-3.3125' to each side of the equation.
3.3125 + -3.3125 + x = -4.194956049 + -3.3125

Combine like terms: 3.3125 + -3.3125 = 0.0000
0.0000 + x = -4.194956049 + -3.3125
x = -4.194956049 + -3.3125

Combine like terms: -4.194956049 + -3.3125 = -7.507456049
x = -7.507456049

Simplifying
x = -7.507456049


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.882456049, -7.507456049}

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