2.2x^2+6.7x-6.5=0

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Solution for 2.2x^2+6.7x-6.5=0 equation: 


Simplifying
2.2x2 + 6.7x + -6.5 = 0

Reorder the terms:
-6.5 + 6.7x + 2.2x2 = 0

Solving
-6.5 + 6.7x + 2.2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2.2'.
-2.954545455 + 3.045454545x + x2 = 0

Move the constant term to the right:

Add '2.954545455' to each side of the equation.
-2.954545455 + 3.045454545x + 2.954545455 + x2 = 0 + 2.954545455

Reorder the terms:
-2.954545455 + 2.954545455 + 3.045454545x + x2 = 0 + 2.954545455

Combine like terms: -2.954545455 + 2.954545455 = 0.000000000
0.000000000 + 3.045454545x + x2 = 0 + 2.954545455
3.045454545x + x2 = 0 + 2.954545455

Combine like terms: 0 + 2.954545455 = 2.954545455
3.045454545x + x2 = 2.954545455

The x term is 3.045454545x.  Take half its coefficient (1.522727273).
Square it (2.318698348) and add it to both sides.

Add '2.318698348' to each side of the equation.
3.045454545x + 2.318698348 + x2 = 2.954545455 + 2.318698348

Reorder the terms:
2.318698348 + 3.045454545x + x2 = 2.954545455 + 2.318698348

Combine like terms: 2.954545455 + 2.318698348 = 5.273243803
2.318698348 + 3.045454545x + x2 = 5.273243803

Factor a perfect square on the left side:
(x + 1.522727273)(x + 1.522727273) = 5.273243803

Calculate the square root of the right side: 2.296354459

Break this problem into two subproblems by setting 
(x + 1.522727273) equal to 2.296354459 and -2.296354459.


Subproblem 1
x + 1.522727273 = 2.296354459

Simplifying
x + 1.522727273 = 2.296354459

Reorder the terms:
1.522727273 + x = 2.296354459

Solving
1.522727273 + x = 2.296354459

Solving for variable 'x'.

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

Add '-1.522727273' to each side of the equation.
1.522727273 + -1.522727273 + x = 2.296354459 + -1.522727273

Combine like terms: 1.522727273 + -1.522727273 = 0.000000000
0.000000000 + x = 2.296354459 + -1.522727273
x = 2.296354459 + -1.522727273

Combine like terms: 2.296354459 + -1.522727273 = 0.773627186
x = 0.773627186

Simplifying
x = 0.773627186


Subproblem 2
x + 1.522727273 = -2.296354459

Simplifying
x + 1.522727273 = -2.296354459

Reorder the terms:
1.522727273 + x = -2.296354459

Solving
1.522727273 + x = -2.296354459

Solving for variable 'x'.

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

Add '-1.522727273' to each side of the equation.
1.522727273 + -1.522727273 + x = -2.296354459 + -1.522727273

Combine like terms: 1.522727273 + -1.522727273 = 0.000000000
0.000000000 + x = -2.296354459 + -1.522727273
x = -2.296354459 + -1.522727273

Combine like terms: -2.296354459 + -1.522727273 = -3.819081732
x = -3.819081732

Simplifying
x = -3.819081732


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.773627186, -3.819081732}

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