2x^2+27x-7.5=0

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Solution for 2x^2+27x-7.5=0 equation: 


Simplifying
2x2 + 27x + -7.5 = 0

Reorder the terms:
-7.5 + 27x + 2x2 = 0

Solving
-7.5 + 27x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
-3.75 + 13.5x + x2 = 0

Move the constant term to the right:

Add '3.75' to each side of the equation.
-3.75 + 13.5x + 3.75 + x2 = 0 + 3.75

Reorder the terms:
-3.75 + 3.75 + 13.5x + x2 = 0 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + 13.5x + x2 = 0 + 3.75
13.5x + x2 = 0 + 3.75

Combine like terms: 0 + 3.75 = 3.75
13.5x + x2 = 3.75

The x term is 13.5x.  Take half its coefficient (6.75).
Square it (45.5625) and add it to both sides.

Add '45.5625' to each side of the equation.
13.5x + 45.5625 + x2 = 3.75 + 45.5625

Reorder the terms:
45.5625 + 13.5x + x2 = 3.75 + 45.5625

Combine like terms: 3.75 + 45.5625 = 49.3125
45.5625 + 13.5x + x2 = 49.3125

Factor a perfect square on the left side:
(x + 6.75)(x + 6.75) = 49.3125

Calculate the square root of the right side: 7.022285953

Break this problem into two subproblems by setting 
(x + 6.75) equal to 7.022285953 and -7.022285953.


Subproblem 1
x + 6.75 = 7.022285953

Simplifying
x + 6.75 = 7.022285953

Reorder the terms:
6.75 + x = 7.022285953

Solving
6.75 + x = 7.022285953

Solving for variable 'x'.

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

Add '-6.75' to each side of the equation.
6.75 + -6.75 + x = 7.022285953 + -6.75

Combine like terms: 6.75 + -6.75 = 0.00
0.00 + x = 7.022285953 + -6.75
x = 7.022285953 + -6.75

Combine like terms: 7.022285953 + -6.75 = 0.272285953
x = 0.272285953

Simplifying
x = 0.272285953


Subproblem 2
x + 6.75 = -7.022285953

Simplifying
x + 6.75 = -7.022285953

Reorder the terms:
6.75 + x = -7.022285953

Solving
6.75 + x = -7.022285953

Solving for variable 'x'.

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

Add '-6.75' to each side of the equation.
6.75 + -6.75 + x = -7.022285953 + -6.75

Combine like terms: 6.75 + -6.75 = 0.00
0.00 + x = -7.022285953 + -6.75
x = -7.022285953 + -6.75

Combine like terms: -7.022285953 + -6.75 = -13.772285953
x = -13.772285953

Simplifying
x = -13.772285953


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.272285953, -13.772285953}

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