2(2x^2-33x+75)=0

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Solution for 2(2x^2-33x+75)=0 equation: 


Simplifying
2(2x2 + -33x + 75) = 0

Reorder the terms:
2(75 + -33x + 2x2) = 0
(75 * 2 + -33x * 2 + 2x2 * 2) = 0
(150 + -66x + 4x2) = 0

Solving
150 + -66x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(75 + -33x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(75 + -33x + 2x2)' equal to zero and attempt to solve:

Simplifying
75 + -33x + 2x2 = 0

Solving
75 + -33x + 2x2 = 0

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

Divide each side by '2'.
37.5 + -16.5x + x2 = 0

Move the constant term to the right:

Add '-37.5' to each side of the equation.
37.5 + -16.5x + -37.5 + x2 = 0 + -37.5

Reorder the terms:
37.5 + -37.5 + -16.5x + x2 = 0 + -37.5

Combine like terms: 37.5 + -37.5 = 0.0
0.0 + -16.5x + x2 = 0 + -37.5
-16.5x + x2 = 0 + -37.5

Combine like terms: 0 + -37.5 = -37.5
-16.5x + x2 = -37.5

The x term is -16.5x.  Take half its coefficient (-8.25).
Square it (68.0625) and add it to both sides.

Add '68.0625' to each side of the equation.
-16.5x + 68.0625 + x2 = -37.5 + 68.0625

Reorder the terms:
68.0625 + -16.5x + x2 = -37.5 + 68.0625

Combine like terms: -37.5 + 68.0625 = 30.5625
68.0625 + -16.5x + x2 = 30.5625

Factor a perfect square on the left side:
(x + -8.25)(x + -8.25) = 30.5625

Calculate the square root of the right side: 5.528336097

Break this problem into two subproblems by setting 
(x + -8.25) equal to 5.528336097 and -5.528336097.


Subproblem 1
x + -8.25 = 5.528336097

Simplifying
x + -8.25 = 5.528336097

Reorder the terms:
-8.25 + x = 5.528336097

Solving
-8.25 + x = 5.528336097

Solving for variable 'x'.

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

Add '8.25' to each side of the equation.
-8.25 + 8.25 + x = 5.528336097 + 8.25

Combine like terms: -8.25 + 8.25 = 0.00
0.00 + x = 5.528336097 + 8.25
x = 5.528336097 + 8.25

Combine like terms: 5.528336097 + 8.25 = 13.778336097
x = 13.778336097

Simplifying
x = 13.778336097


Subproblem 2
x + -8.25 = -5.528336097

Simplifying
x + -8.25 = -5.528336097

Reorder the terms:
-8.25 + x = -5.528336097

Solving
-8.25 + x = -5.528336097

Solving for variable 'x'.

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

Add '8.25' to each side of the equation.
-8.25 + 8.25 + x = -5.528336097 + 8.25

Combine like terms: -8.25 + 8.25 = 0.00
0.00 + x = -5.528336097 + 8.25
x = -5.528336097 + 8.25

Combine like terms: -5.528336097 + 8.25 = 2.721663903
x = 2.721663903

Simplifying
x = 2.721663903


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.778336097, 2.721663903}
Solution
x = {13.778336097, 2.721663903}

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