9x^2-72x-27=0

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Solution for 9x^2-72x-27=0 equation: 


Simplifying
9x2 + -72x + -27 = 0

Reorder the terms:
-27 + -72x + 9x2 = 0

Solving
-27 + -72x + 9x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '9'.
9(-3 + -8x + x2) = 0

Ignore the factor 9.

Subproblem 1
Set the factor '(-3 + -8x + x2)' equal to zero and attempt to solve:

Simplifying
-3 + -8x + x2 = 0

Solving
-3 + -8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -8x + 3 + x2 = 0 + 3

Reorder the terms:
-3 + 3 + -8x + x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -8x + x2 = 0 + 3
-8x + x2 = 0 + 3

Combine like terms: 0 + 3 = 3
-8x + x2 = 3

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = 3 + 16

Reorder the terms:
16 + -8x + x2 = 3 + 16

Combine like terms: 3 + 16 = 19
16 + -8x + x2 = 19

Factor a perfect square on the left side:
(x + -4)(x + -4) = 19

Calculate the square root of the right side: 4.358898944

Break this problem into two subproblems by setting 
(x + -4) equal to 4.358898944 and -4.358898944.


Subproblem 1
x + -4 = 4.358898944

Simplifying
x + -4 = 4.358898944

Reorder the terms:
-4 + x = 4.358898944

Solving
-4 + x = 4.358898944

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = 4.358898944 + 4

Combine like terms: -4 + 4 = 0
0 + x = 4.358898944 + 4
x = 4.358898944 + 4

Combine like terms: 4.358898944 + 4 = 8.358898944
x = 8.358898944

Simplifying
x = 8.358898944


Subproblem 2
x + -4 = -4.358898944

Simplifying
x + -4 = -4.358898944

Reorder the terms:
-4 + x = -4.358898944

Solving
-4 + x = -4.358898944

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = -4.358898944 + 4

Combine like terms: -4 + 4 = 0
0 + x = -4.358898944 + 4
x = -4.358898944 + 4

Combine like terms: -4.358898944 + 4 = -0.358898944
x = -0.358898944

Simplifying
x = -0.358898944


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.358898944, -0.358898944}
Solution
x = {8.358898944, -0.358898944}

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