6x^2-30x-204=0

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Solution for 6x^2-30x-204=0 equation: 


Simplifying
6x2 + -30x + -204 = 0

Reorder the terms:
-204 + -30x + 6x2 = 0

Solving
-204 + -30x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-34 + -5x + x2) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(-34 + -5x + x2)' equal to zero and attempt to solve:

Simplifying
-34 + -5x + x2 = 0

Solving
-34 + -5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '34' to each side of the equation.
-34 + -5x + 34 + x2 = 0 + 34

Reorder the terms:
-34 + 34 + -5x + x2 = 0 + 34

Combine like terms: -34 + 34 = 0
0 + -5x + x2 = 0 + 34
-5x + x2 = 0 + 34

Combine like terms: 0 + 34 = 34
-5x + x2 = 34

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 34 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 34 + 6.25

Combine like terms: 34 + 6.25 = 40.25
6.25 + -5x + x2 = 40.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 40.25

Calculate the square root of the right side: 6.34428877

Break this problem into two subproblems by setting 
(x + -2.5) equal to 6.34428877 and -6.34428877.


Subproblem 1
x + -2.5 = 6.34428877

Simplifying
x + -2.5 = 6.34428877

Reorder the terms:
-2.5 + x = 6.34428877

Solving
-2.5 + x = 6.34428877

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 6.34428877 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 6.34428877 + 2.5
x = 6.34428877 + 2.5

Combine like terms: 6.34428877 + 2.5 = 8.84428877
x = 8.84428877

Simplifying
x = 8.84428877


Subproblem 2
x + -2.5 = -6.34428877

Simplifying
x + -2.5 = -6.34428877

Reorder the terms:
-2.5 + x = -6.34428877

Solving
-2.5 + x = -6.34428877

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -6.34428877 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -6.34428877 + 2.5
x = -6.34428877 + 2.5

Combine like terms: -6.34428877 + 2.5 = -3.84428877
x = -3.84428877

Simplifying
x = -3.84428877


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.84428877, -3.84428877}
Solution
x = {8.84428877, -3.84428877}

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