4x^2-68x-204=0

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Solution for 4x^2-68x-204=0 equation: 


Simplifying
4x2 + -68x + -204 = 0

Reorder the terms:
-204 + -68x + 4x2 = 0

Solving
-204 + -68x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-51 + -17x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-51 + -17x + x2)' equal to zero and attempt to solve:

Simplifying
-51 + -17x + x2 = 0

Solving
-51 + -17x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '51' to each side of the equation.
-51 + -17x + 51 + x2 = 0 + 51

Reorder the terms:
-51 + 51 + -17x + x2 = 0 + 51

Combine like terms: -51 + 51 = 0
0 + -17x + x2 = 0 + 51
-17x + x2 = 0 + 51

Combine like terms: 0 + 51 = 51
-17x + x2 = 51

The x term is -17x.  Take half its coefficient (-8.5).
Square it (72.25) and add it to both sides.

Add '72.25' to each side of the equation.
-17x + 72.25 + x2 = 51 + 72.25

Reorder the terms:
72.25 + -17x + x2 = 51 + 72.25

Combine like terms: 51 + 72.25 = 123.25
72.25 + -17x + x2 = 123.25

Factor a perfect square on the left side:
(x + -8.5)(x + -8.5) = 123.25

Calculate the square root of the right side: 11.101801656

Break this problem into two subproblems by setting 
(x + -8.5) equal to 11.101801656 and -11.101801656.


Subproblem 1
x + -8.5 = 11.101801656

Simplifying
x + -8.5 = 11.101801656

Reorder the terms:
-8.5 + x = 11.101801656

Solving
-8.5 + x = 11.101801656

Solving for variable 'x'.

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

Add '8.5' to each side of the equation.
-8.5 + 8.5 + x = 11.101801656 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + x = 11.101801656 + 8.5
x = 11.101801656 + 8.5

Combine like terms: 11.101801656 + 8.5 = 19.601801656
x = 19.601801656

Simplifying
x = 19.601801656


Subproblem 2
x + -8.5 = -11.101801656

Simplifying
x + -8.5 = -11.101801656

Reorder the terms:
-8.5 + x = -11.101801656

Solving
-8.5 + x = -11.101801656

Solving for variable 'x'.

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

Add '8.5' to each side of the equation.
-8.5 + 8.5 + x = -11.101801656 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + x = -11.101801656 + 8.5
x = -11.101801656 + 8.5

Combine like terms: -11.101801656 + 8.5 = -2.601801656
x = -2.601801656

Simplifying
x = -2.601801656


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {19.601801656, -2.601801656}
Solution
x = {19.601801656, -2.601801656}

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