-2.7x^2+40x+6.5=0

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Solution for -2.7x^2+40x+6.5=0 equation: 


Simplifying
-2.7x2 + 40x + 6.5 = 0

Reorder the terms:
6.5 + 40x + -2.7x2 = 0

Solving
6.5 + 40x + -2.7x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-2.7 the coefficient of the squared term: 

Divide each side by '-2.7'.
-2.407407407 + -14.81481481x + x2 = 0

Move the constant term to the right:

Add '2.407407407' to each side of the equation.
-2.407407407 + -14.81481481x + 2.407407407 + x2 = 0 + 2.407407407

Reorder the terms:
-2.407407407 + 2.407407407 + -14.81481481x + x2 = 0 + 2.407407407

Combine like terms: -2.407407407 + 2.407407407 = 0.000000000
0.000000000 + -14.81481481x + x2 = 0 + 2.407407407
-14.81481481x + x2 = 0 + 2.407407407

Combine like terms: 0 + 2.407407407 = 2.407407407
-14.81481481x + x2 = 2.407407407

The x term is -14.81481481x.  Take half its coefficient (-7.407407405).
Square it (54.86968446) and add it to both sides.

Add '54.86968446' to each side of the equation.
-14.81481481x + 54.86968446 + x2 = 2.407407407 + 54.86968446

Reorder the terms:
54.86968446 + -14.81481481x + x2 = 2.407407407 + 54.86968446

Combine like terms: 2.407407407 + 54.86968446 = 57.277091867
54.86968446 + -14.81481481x + x2 = 57.277091867

Factor a perfect square on the left side:
(x + -7.407407405)(x + -7.407407405) = 57.277091867

Calculate the square root of the right side: 7.568163044

Break this problem into two subproblems by setting 
(x + -7.407407405) equal to 7.568163044 and -7.568163044.


Subproblem 1
x + -7.407407405 = 7.568163044

Simplifying
x + -7.407407405 = 7.568163044

Reorder the terms:
-7.407407405 + x = 7.568163044

Solving
-7.407407405 + x = 7.568163044

Solving for variable 'x'.

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

Add '7.407407405' to each side of the equation.
-7.407407405 + 7.407407405 + x = 7.568163044 + 7.407407405

Combine like terms: -7.407407405 + 7.407407405 = 0.000000000
0.000000000 + x = 7.568163044 + 7.407407405
x = 7.568163044 + 7.407407405

Combine like terms: 7.568163044 + 7.407407405 = 14.975570449
x = 14.975570449

Simplifying
x = 14.975570449


Subproblem 2
x + -7.407407405 = -7.568163044

Simplifying
x + -7.407407405 = -7.568163044

Reorder the terms:
-7.407407405 + x = -7.568163044

Solving
-7.407407405 + x = -7.568163044

Solving for variable 'x'.

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

Add '7.407407405' to each side of the equation.
-7.407407405 + 7.407407405 + x = -7.568163044 + 7.407407405

Combine like terms: -7.407407405 + 7.407407405 = 0.000000000
0.000000000 + x = -7.568163044 + 7.407407405
x = -7.568163044 + 7.407407405

Combine like terms: -7.568163044 + 7.407407405 = -0.160755639
x = -0.160755639

Simplifying
x = -0.160755639


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.975570449, -0.160755639}

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