0=-204+16x+4x^2

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Solution for 0=-204+16x+4x^2 equation: 


Simplifying
0 = -204 + 16x + 4x2

Solving
0 = -204 + 16x + 4x2

Solving for variable 'x'.

Combine like terms: 0 + 204 = 204
204 + -16x + -4x2 = -204 + 16x + 4x2 + 204 + -16x + -4x2

Reorder the terms:
204 + -16x + -4x2 = -204 + 204 + 16x + -16x + 4x2 + -4x2

Combine like terms: -204 + 204 = 0
204 + -16x + -4x2 = 0 + 16x + -16x + 4x2 + -4x2
204 + -16x + -4x2 = 16x + -16x + 4x2 + -4x2

Combine like terms: 16x + -16x = 0
204 + -16x + -4x2 = 0 + 4x2 + -4x2
204 + -16x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
204 + -16x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(51 + -4x + -1x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(51 + -4x + -1x2)' equal to zero and attempt to solve:

Simplifying
51 + -4x + -1x2 = 0

Solving
51 + -4x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-51 + 4x + x2 = 0

Move the constant term to the right:

Add '51' to each side of the equation.
-51 + 4x + 51 + x2 = 0 + 51

Reorder the terms:
-51 + 51 + 4x + x2 = 0 + 51

Combine like terms: -51 + 51 = 0
0 + 4x + x2 = 0 + 51
4x + x2 = 0 + 51

Combine like terms: 0 + 51 = 51
4x + x2 = 51

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 51 + 4

Reorder the terms:
4 + 4x + x2 = 51 + 4

Combine like terms: 51 + 4 = 55
4 + 4x + x2 = 55

Factor a perfect square on the left side:
(x + 2)(x + 2) = 55

Calculate the square root of the right side: 7.416198487

Break this problem into two subproblems by setting 
(x + 2) equal to 7.416198487 and -7.416198487.


Subproblem 1
x + 2 = 7.416198487

Simplifying
x + 2 = 7.416198487

Reorder the terms:
2 + x = 7.416198487

Solving
2 + x = 7.416198487

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 7.416198487 + -2

Combine like terms: 2 + -2 = 0
0 + x = 7.416198487 + -2
x = 7.416198487 + -2

Combine like terms: 7.416198487 + -2 = 5.416198487
x = 5.416198487

Simplifying
x = 5.416198487


Subproblem 2
x + 2 = -7.416198487

Simplifying
x + 2 = -7.416198487

Reorder the terms:
2 + x = -7.416198487

Solving
2 + x = -7.416198487

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -7.416198487 + -2

Combine like terms: 2 + -2 = 0
0 + x = -7.416198487 + -2
x = -7.416198487 + -2

Combine like terms: -7.416198487 + -2 = -9.416198487
x = -9.416198487

Simplifying
x = -9.416198487


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.416198487, -9.416198487}
Solution
x = {5.416198487, -9.416198487}

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