-16x^2+264x+5=0

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Solution for -16x^2+264x+5=0 equation: 


Simplifying
-16x2 + 264x + 5 = 0

Reorder the terms:
5 + 264x + -16x2 = 0

Solving
5 + 264x + -16x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-16 the coefficient of the squared term: 

Divide each side by '-16'.
-0.3125 + -16.5x + x2 = 0

Move the constant term to the right:

Add '0.3125' to each side of the equation.
-0.3125 + -16.5x + 0.3125 + x2 = 0 + 0.3125

Reorder the terms:
-0.3125 + 0.3125 + -16.5x + x2 = 0 + 0.3125

Combine like terms: -0.3125 + 0.3125 = 0.0000
0.0000 + -16.5x + x2 = 0 + 0.3125
-16.5x + x2 = 0 + 0.3125

Combine like terms: 0 + 0.3125 = 0.3125
-16.5x + x2 = 0.3125

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 = 0.3125 + 68.0625

Reorder the terms:
68.0625 + -16.5x + x2 = 0.3125 + 68.0625

Combine like terms: 0.3125 + 68.0625 = 68.375
68.0625 + -16.5x + x2 = 68.375

Factor a perfect square on the left side:
(x + -8.25)(x + -8.25) = 68.375

Calculate the square root of the right side: 8.268917704

Break this problem into two subproblems by setting 
(x + -8.25) equal to 8.268917704 and -8.268917704.


Subproblem 1
x + -8.25 = 8.268917704

Simplifying
x + -8.25 = 8.268917704

Reorder the terms:
-8.25 + x = 8.268917704

Solving
-8.25 + x = 8.268917704

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 = 8.268917704 + 8.25

Combine like terms: -8.25 + 8.25 = 0.00
0.00 + x = 8.268917704 + 8.25
x = 8.268917704 + 8.25

Combine like terms: 8.268917704 + 8.25 = 16.518917704
x = 16.518917704

Simplifying
x = 16.518917704


Subproblem 2
x + -8.25 = -8.268917704

Simplifying
x + -8.25 = -8.268917704

Reorder the terms:
-8.25 + x = -8.268917704

Solving
-8.25 + x = -8.268917704

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 = -8.268917704 + 8.25

Combine like terms: -8.25 + 8.25 = 0.00
0.00 + x = -8.268917704 + 8.25
x = -8.268917704 + 8.25

Combine like terms: -8.268917704 + 8.25 = -0.018917704
x = -0.018917704

Simplifying
x = -0.018917704


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.518917704, -0.018917704}

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