16x^2-320x-816=0

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Solution for 16x^2-320x-816=0 equation: 


Simplifying
16x2 + -320x + -816 = 0

Reorder the terms:
-816 + -320x + 16x2 = 0

Solving
-816 + -320x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '16'.
16(-51 + -20x + x2) = 0

Ignore the factor 16.

Subproblem 1
Set the factor '(-51 + -20x + x2)' equal to zero and attempt to solve:

Simplifying
-51 + -20x + x2 = 0

Solving
-51 + -20x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '51' to each side of the equation.
-51 + -20x + 51 + x2 = 0 + 51

Reorder the terms:
-51 + 51 + -20x + x2 = 0 + 51

Combine like terms: -51 + 51 = 0
0 + -20x + x2 = 0 + 51
-20x + x2 = 0 + 51

Combine like terms: 0 + 51 = 51
-20x + x2 = 51

The x term is -20x.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20x + 100 + x2 = 51 + 100

Reorder the terms:
100 + -20x + x2 = 51 + 100

Combine like terms: 51 + 100 = 151
100 + -20x + x2 = 151

Factor a perfect square on the left side:
(x + -10)(x + -10) = 151

Calculate the square root of the right side: 12.288205727

Break this problem into two subproblems by setting 
(x + -10) equal to 12.288205727 and -12.288205727.


Subproblem 1
x + -10 = 12.288205727

Simplifying
x + -10 = 12.288205727

Reorder the terms:
-10 + x = 12.288205727

Solving
-10 + x = 12.288205727

Solving for variable 'x'.

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

Add '10' to each side of the equation.
-10 + 10 + x = 12.288205727 + 10

Combine like terms: -10 + 10 = 0
0 + x = 12.288205727 + 10
x = 12.288205727 + 10

Combine like terms: 12.288205727 + 10 = 22.288205727
x = 22.288205727

Simplifying
x = 22.288205727


Subproblem 2
x + -10 = -12.288205727

Simplifying
x + -10 = -12.288205727

Reorder the terms:
-10 + x = -12.288205727

Solving
-10 + x = -12.288205727

Solving for variable 'x'.

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

Add '10' to each side of the equation.
-10 + 10 + x = -12.288205727 + 10

Combine like terms: -10 + 10 = 0
0 + x = -12.288205727 + 10
x = -12.288205727 + 10

Combine like terms: -12.288205727 + 10 = -2.288205727
x = -2.288205727

Simplifying
x = -2.288205727


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {22.288205727, -2.288205727}
Solution
x = {22.288205727, -2.288205727}

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