6x^2-33x-75=0

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Solution for 6x^2-33x-75=0 equation: 


Simplifying
6x2 + -33x + -75 = 0

Reorder the terms:
-75 + -33x + 6x2 = 0

Solving
-75 + -33x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-25 + -11x + 2x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-25 + -11x + 2x2)' equal to zero and attempt to solve:

Simplifying
-25 + -11x + 2x2 = 0

Solving
-25 + -11x + 2x2 = 0

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

Divide each side by '2'.
-12.5 + -5.5x + x2 = 0

Move the constant term to the right:

Add '12.5' to each side of the equation.
-12.5 + -5.5x + 12.5 + x2 = 0 + 12.5

Reorder the terms:
-12.5 + 12.5 + -5.5x + x2 = 0 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + -5.5x + x2 = 0 + 12.5
-5.5x + x2 = 0 + 12.5

Combine like terms: 0 + 12.5 = 12.5
-5.5x + x2 = 12.5

The x term is -5.5x.  Take half its coefficient (-2.75).
Square it (7.5625) and add it to both sides.

Add '7.5625' to each side of the equation.
-5.5x + 7.5625 + x2 = 12.5 + 7.5625

Reorder the terms:
7.5625 + -5.5x + x2 = 12.5 + 7.5625

Combine like terms: 12.5 + 7.5625 = 20.0625
7.5625 + -5.5x + x2 = 20.0625

Factor a perfect square on the left side:
(x + -2.75)(x + -2.75) = 20.0625

Calculate the square root of the right side: 4.479118217

Break this problem into two subproblems by setting 
(x + -2.75) equal to 4.479118217 and -4.479118217.


Subproblem 1
x + -2.75 = 4.479118217

Simplifying
x + -2.75 = 4.479118217

Reorder the terms:
-2.75 + x = 4.479118217

Solving
-2.75 + x = 4.479118217

Solving for variable 'x'.

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

Add '2.75' to each side of the equation.
-2.75 + 2.75 + x = 4.479118217 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + x = 4.479118217 + 2.75
x = 4.479118217 + 2.75

Combine like terms: 4.479118217 + 2.75 = 7.229118217
x = 7.229118217

Simplifying
x = 7.229118217


Subproblem 2
x + -2.75 = -4.479118217

Simplifying
x + -2.75 = -4.479118217

Reorder the terms:
-2.75 + x = -4.479118217

Solving
-2.75 + x = -4.479118217

Solving for variable 'x'.

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

Add '2.75' to each side of the equation.
-2.75 + 2.75 + x = -4.479118217 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + x = -4.479118217 + 2.75
x = -4.479118217 + 2.75

Combine like terms: -4.479118217 + 2.75 = -1.729118217
x = -1.729118217

Simplifying
x = -1.729118217


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.229118217, -1.729118217}
Solution
x = {7.229118217, -1.729118217}

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