9x^2-72x+84=0

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Solution for 9x^2-72x+84=0 equation: 


Simplifying
9x2 + -72x + 84 = 0

Reorder the terms:
84 + -72x + 9x2 = 0

Solving
84 + -72x + 9x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(28 + -24x + 3x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(28 + -24x + 3x2)' equal to zero and attempt to solve:

Simplifying
28 + -24x + 3x2 = 0

Solving
28 + -24x + 3x2 = 0

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

Divide each side by '3'.
9.333333333 + -8x + x2 = 0

Move the constant term to the right:

Add '-9.333333333' to each side of the equation.
9.333333333 + -8x + -9.333333333 + x2 = 0 + -9.333333333

Reorder the terms:
9.333333333 + -9.333333333 + -8x + x2 = 0 + -9.333333333

Combine like terms: 9.333333333 + -9.333333333 = 0.000000000
0.000000000 + -8x + x2 = 0 + -9.333333333
-8x + x2 = 0 + -9.333333333

Combine like terms: 0 + -9.333333333 = -9.333333333
-8x + x2 = -9.333333333

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 = -9.333333333 + 16

Reorder the terms:
16 + -8x + x2 = -9.333333333 + 16

Combine like terms: -9.333333333 + 16 = 6.666666667
16 + -8x + x2 = 6.666666667

Factor a perfect square on the left side:
(x + -4)(x + -4) = 6.666666667

Calculate the square root of the right side: 2.581988898

Break this problem into two subproblems by setting 
(x + -4) equal to 2.581988898 and -2.581988898.


Subproblem 1
x + -4 = 2.581988898

Simplifying
x + -4 = 2.581988898

Reorder the terms:
-4 + x = 2.581988898

Solving
-4 + x = 2.581988898

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 = 2.581988898 + 4

Combine like terms: -4 + 4 = 0
0 + x = 2.581988898 + 4
x = 2.581988898 + 4

Combine like terms: 2.581988898 + 4 = 6.581988898
x = 6.581988898

Simplifying
x = 6.581988898


Subproblem 2
x + -4 = -2.581988898

Simplifying
x + -4 = -2.581988898

Reorder the terms:
-4 + x = -2.581988898

Solving
-4 + x = -2.581988898

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 = -2.581988898 + 4

Combine like terms: -4 + 4 = 0
0 + x = -2.581988898 + 4
x = -2.581988898 + 4

Combine like terms: -2.581988898 + 4 = 1.418011102
x = 1.418011102

Simplifying
x = 1.418011102


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.581988898, 1.418011102}
Solution
x = {6.581988898, 1.418011102}

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