-2.7x^2+30x+6.5=

Solution for -2.7x^2+30x+6.5= equation:

Simplifying
-2.7x2 + 30x + 6.5 = 0

Reorder the terms:
6.5 + 30x + -2.7x2 = 0

Solving
6.5 + 30x + -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 + -11.11111111x + x2 = 0

Move the constant term to the right:

Add '2.407407407' to each side of the equation.
-2.407407407 + -11.11111111x + 2.407407407 + x2 = 0 + 2.407407407

Reorder the terms:
-2.407407407 + 2.407407407 + -11.11111111x + x2 = 0 + 2.407407407

Combine like terms: -2.407407407 + 2.407407407 = 0.000000000
0.000000000 + -11.11111111x + x2 = 0 + 2.407407407
-11.11111111x + x2 = 0 + 2.407407407

Combine like terms: 0 + 2.407407407 = 2.407407407
-11.11111111x + x2 = 2.407407407

The x term is -11.11111111x.  Take half its coefficient (-5.555555555).
Square it (30.86419752) and add it to both sides.

Add '30.86419752' to each side of the equation.
-11.11111111x + 30.86419752 + x2 = 2.407407407 + 30.86419752

Reorder the terms:
30.86419752 + -11.11111111x + x2 = 2.407407407 + 30.86419752

Combine like terms: 2.407407407 + 30.86419752 = 33.271604927
30.86419752 + -11.11111111x + x2 = 33.271604927

Factor a perfect square on the left side:
(x + -5.555555555)(x + -5.555555555) = 33.271604927

Calculate the square root of the right side: 5.768154378

Break this problem into two subproblems by setting 
(x + -5.555555555) equal to 5.768154378 and -5.768154378.

Subproblem 1
x + -5.555555555 = 5.768154378

Simplifying
x + -5.555555555 = 5.768154378

Reorder the terms:
-5.555555555 + x = 5.768154378

Solving
-5.555555555 + x = 5.768154378

Solving for variable 'x'.

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

Add '5.555555555' to each side of the equation.
-5.555555555 + 5.555555555 + x = 5.768154378 + 5.555555555

Combine like terms: -5.555555555 + 5.555555555 = 0.000000000
0.000000000 + x = 5.768154378 + 5.555555555
x = 5.768154378 + 5.555555555

Combine like terms: 5.768154378 + 5.555555555 = 11.323709933
x = 11.323709933

Simplifying
x = 11.323709933

Subproblem 2
x + -5.555555555 = -5.768154378

Simplifying
x + -5.555555555 = -5.768154378

Reorder the terms:
-5.555555555 + x = -5.768154378

Solving
-5.555555555 + x = -5.768154378

Solving for variable 'x'.

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

Add '5.555555555' to each side of the equation.
-5.555555555 + 5.555555555 + x = -5.768154378 + 5.555555555

Combine like terms: -5.555555555 + 5.555555555 = 0.000000000
0.000000000 + x = -5.768154378 + 5.555555555
x = -5.768154378 + 5.555555555

Combine like terms: -5.768154378 + 5.555555555 = -0.212598823
x = -0.212598823

Simplifying
x = -0.212598823

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.323709933, -0.212598823}