2x^2+27x-40=0

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Solution for 2x^2+27x-40=0 equation: 


Simplifying
2x2 + 27x + -40 = 0

Reorder the terms:
-40 + 27x + 2x2 = 0

Solving
-40 + 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'.
-20 + 13.5x + x2 = 0

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + 13.5x + 20 + x2 = 0 + 20

Reorder the terms:
-20 + 20 + 13.5x + x2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + 13.5x + x2 = 0 + 20
13.5x + x2 = 0 + 20

Combine like terms: 0 + 20 = 20
13.5x + x2 = 20

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 = 20 + 45.5625

Reorder the terms:
45.5625 + 13.5x + x2 = 20 + 45.5625

Combine like terms: 20 + 45.5625 = 65.5625
45.5625 + 13.5x + x2 = 65.5625

Factor a perfect square on the left side:
(x + 6.75)(x + 6.75) = 65.5625

Calculate the square root of the right side: 8.09706737

Break this problem into two subproblems by setting 
(x + 6.75) equal to 8.09706737 and -8.09706737.


Subproblem 1
x + 6.75 = 8.09706737

Simplifying
x + 6.75 = 8.09706737

Reorder the terms:
6.75 + x = 8.09706737

Solving
6.75 + x = 8.09706737

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 = 8.09706737 + -6.75

Combine like terms: 6.75 + -6.75 = 0.00
0.00 + x = 8.09706737 + -6.75
x = 8.09706737 + -6.75

Combine like terms: 8.09706737 + -6.75 = 1.34706737
x = 1.34706737

Simplifying
x = 1.34706737


Subproblem 2
x + 6.75 = -8.09706737

Simplifying
x + 6.75 = -8.09706737

Reorder the terms:
6.75 + x = -8.09706737

Solving
6.75 + x = -8.09706737

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 = -8.09706737 + -6.75

Combine like terms: 6.75 + -6.75 = 0.00
0.00 + x = -8.09706737 + -6.75
x = -8.09706737 + -6.75

Combine like terms: -8.09706737 + -6.75 = -14.84706737
x = -14.84706737

Simplifying
x = -14.84706737


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.34706737, -14.84706737}

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