x^2+27x-81=0

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Solution for x^2+27x-81=0 equation:


Simplifying
x2 + 27x + -81 = 0

Reorder the terms:
-81 + 27x + x2 = 0

Solving
-81 + 27x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '81' to each side of the equation.
-81 + 27x + 81 + x2 = 0 + 81

Reorder the terms:
-81 + 81 + 27x + x2 = 0 + 81

Combine like terms: -81 + 81 = 0
0 + 27x + x2 = 0 + 81
27x + x2 = 0 + 81

Combine like terms: 0 + 81 = 81
27x + x2 = 81

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 = 81 + 182.25

Reorder the terms:
182.25 + 27x + x2 = 81 + 182.25

Combine like terms: 81 + 182.25 = 263.25
182.25 + 27x + x2 = 263.25

Factor a perfect square on the left side:
(x + 13.5)(x + 13.5) = 263.25

Calculate the square root of the right side: 16.22498074

Break this problem into two subproblems by setting 
(x + 13.5) equal to 16.22498074 and -16.22498074.

Subproblem 1

x + 13.5 = 16.22498074 Simplifying x + 13.5 = 16.22498074 Reorder the terms: 13.5 + x = 16.22498074 Solving 13.5 + x = 16.22498074 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 = 16.22498074 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + x = 16.22498074 + -13.5 x = 16.22498074 + -13.5 Combine like terms: 16.22498074 + -13.5 = 2.72498074 x = 2.72498074 Simplifying x = 2.72498074

Subproblem 2

x + 13.5 = -16.22498074 Simplifying x + 13.5 = -16.22498074 Reorder the terms: 13.5 + x = -16.22498074 Solving 13.5 + x = -16.22498074 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 = -16.22498074 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + x = -16.22498074 + -13.5 x = -16.22498074 + -13.5 Combine like terms: -16.22498074 + -13.5 = -29.72498074 x = -29.72498074 Simplifying x = -29.72498074

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.72498074, -29.72498074}

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