3x^2-16x-1600=0

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Solution for 3x^2-16x-1600=0 equation: 


Simplifying
3x2 + -16x + -1600 = 0

Reorder the terms:
-1600 + -16x + 3x2 = 0

Solving
-1600 + -16x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-533.3333333 + -5.333333333x + x2 = 0

Move the constant term to the right:

Add '533.3333333' to each side of the equation.
-533.3333333 + -5.333333333x + 533.3333333 + x2 = 0 + 533.3333333

Reorder the terms:
-533.3333333 + 533.3333333 + -5.333333333x + x2 = 0 + 533.3333333

Combine like terms: -533.3333333 + 533.3333333 = 0.0000000
0.0000000 + -5.333333333x + x2 = 0 + 533.3333333
-5.333333333x + x2 = 0 + 533.3333333

Combine like terms: 0 + 533.3333333 = 533.3333333
-5.333333333x + x2 = 533.3333333

The x term is -5.333333333x.  Take half its coefficient (-2.666666667).
Square it (7.111111113) and add it to both sides.

Add '7.111111113' to each side of the equation.
-5.333333333x + 7.111111113 + x2 = 533.3333333 + 7.111111113

Reorder the terms:
7.111111113 + -5.333333333x + x2 = 533.3333333 + 7.111111113

Combine like terms: 533.3333333 + 7.111111113 = 540.444444413
7.111111113 + -5.333333333x + x2 = 540.444444413

Factor a perfect square on the left side:
(x + -2.666666667)(x + -2.666666667) = 540.444444413

Calculate the square root of the right side: 23.247461032

Break this problem into two subproblems by setting 
(x + -2.666666667) equal to 23.247461032 and -23.247461032.


Subproblem 1
x + -2.666666667 = 23.247461032

Simplifying
x + -2.666666667 = 23.247461032

Reorder the terms:
-2.666666667 + x = 23.247461032

Solving
-2.666666667 + x = 23.247461032

Solving for variable 'x'.

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

Add '2.666666667' to each side of the equation.
-2.666666667 + 2.666666667 + x = 23.247461032 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + x = 23.247461032 + 2.666666667
x = 23.247461032 + 2.666666667

Combine like terms: 23.247461032 + 2.666666667 = 25.914127699
x = 25.914127699

Simplifying
x = 25.914127699


Subproblem 2
x + -2.666666667 = -23.247461032

Simplifying
x + -2.666666667 = -23.247461032

Reorder the terms:
-2.666666667 + x = -23.247461032

Solving
-2.666666667 + x = -23.247461032

Solving for variable 'x'.

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

Add '2.666666667' to each side of the equation.
-2.666666667 + 2.666666667 + x = -23.247461032 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + x = -23.247461032 + 2.666666667
x = -23.247461032 + 2.666666667

Combine like terms: -23.247461032 + 2.666666667 = -20.580794365
x = -20.580794365

Simplifying
x = -20.580794365


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {25.914127699, -20.580794365}

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