-16x^2+264x+14=0

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Solution for -16x^2+264x+14=0 equation: 


Simplifying
-16x2 + 264x + 14 = 0

Reorder the terms:
14 + 264x + -16x2 = 0

Solving
14 + 264x + -16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(7 + 132x + -8x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(7 + 132x + -8x2)' equal to zero and attempt to solve:

Simplifying
7 + 132x + -8x2 = 0

Solving
7 + 132x + -8x2 = 0

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
-0.875 + -16.5x + x2 = 0

Move the constant term to the right:

Add '0.875' to each side of the equation.
-0.875 + -16.5x + 0.875 + x2 = 0 + 0.875

Reorder the terms:
-0.875 + 0.875 + -16.5x + x2 = 0 + 0.875

Combine like terms: -0.875 + 0.875 = 0.000
0.000 + -16.5x + x2 = 0 + 0.875
-16.5x + x2 = 0 + 0.875

Combine like terms: 0 + 0.875 = 0.875
-16.5x + x2 = 0.875

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 = 0.875 + 68.0625

Reorder the terms:
68.0625 + -16.5x + x2 = 0.875 + 68.0625

Combine like terms: 0.875 + 68.0625 = 68.9375
68.0625 + -16.5x + x2 = 68.9375

Factor a perfect square on the left side:
(x + -8.25)(x + -8.25) = 68.9375

Calculate the square root of the right side: 8.302860953

Break this problem into two subproblems by setting 
(x + -8.25) equal to 8.302860953 and -8.302860953.


Subproblem 1
x + -8.25 = 8.302860953

Simplifying
x + -8.25 = 8.302860953

Reorder the terms:
-8.25 + x = 8.302860953

Solving
-8.25 + x = 8.302860953

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 = 8.302860953 + 8.25

Combine like terms: -8.25 + 8.25 = 0.00
0.00 + x = 8.302860953 + 8.25
x = 8.302860953 + 8.25

Combine like terms: 8.302860953 + 8.25 = 16.552860953
x = 16.552860953

Simplifying
x = 16.552860953


Subproblem 2
x + -8.25 = -8.302860953

Simplifying
x + -8.25 = -8.302860953

Reorder the terms:
-8.25 + x = -8.302860953

Solving
-8.25 + x = -8.302860953

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 = -8.302860953 + 8.25

Combine like terms: -8.25 + 8.25 = 0.00
0.00 + x = -8.302860953 + 8.25
x = -8.302860953 + 8.25

Combine like terms: -8.302860953 + 8.25 = -0.052860953
x = -0.052860953

Simplifying
x = -0.052860953


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.552860953, -0.052860953}
Solution
x = {16.552860953, -0.052860953}

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