x^2-27x-40=0

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


Simplifying
x2 + -27x + -40 = 0

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

Solving
-40 + -27x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '40' to each side of the equation.
-40 + -27x + 40 + x2 = 0 + 40

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

Combine like terms: -40 + 40 = 0
0 + -27x + x2 = 0 + 40
-27x + x2 = 0 + 40

Combine like terms: 0 + 40 = 40
-27x + x2 = 40

The x term is -27x.  Take half its coefficient (-13.5).
Square it (182.25) and add it to both sides.

Add '182.25' to each side of the equation.
-27x + 182.25 + x2 = 40 + 182.25

Reorder the terms:
182.25 + -27x + x2 = 40 + 182.25

Combine like terms: 40 + 182.25 = 222.25
182.25 + -27x + x2 = 222.25

Factor a perfect square on the left side:
(x + -13.5)(x + -13.5) = 222.25

Calculate the square root of the right side: 14.908051516

Break this problem into two subproblems by setting 
(x + -13.5) equal to 14.908051516 and -14.908051516.


Subproblem 1
x + -13.5 = 14.908051516

Simplifying
x + -13.5 = 14.908051516

Reorder the terms:
-13.5 + x = 14.908051516

Solving
-13.5 + x = 14.908051516

Solving for variable 'x'.

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

Add '13.5' to each side of the equation.
-13.5 + 13.5 + x = 14.908051516 + 13.5

Combine like terms: -13.5 + 13.5 = 0.0
0.0 + x = 14.908051516 + 13.5
x = 14.908051516 + 13.5

Combine like terms: 14.908051516 + 13.5 = 28.408051516
x = 28.408051516

Simplifying
x = 28.408051516


Subproblem 2
x + -13.5 = -14.908051516

Simplifying
x + -13.5 = -14.908051516

Reorder the terms:
-13.5 + x = -14.908051516

Solving
-13.5 + x = -14.908051516

Solving for variable 'x'.

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

Add '13.5' to each side of the equation.
-13.5 + 13.5 + x = -14.908051516 + 13.5

Combine like terms: -13.5 + 13.5 = 0.0
0.0 + x = -14.908051516 + 13.5
x = -14.908051516 + 13.5

Combine like terms: -14.908051516 + 13.5 = -1.408051516
x = -1.408051516

Simplifying
x = -1.408051516


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {28.408051516, -1.408051516}

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