3x^2-28x-481=0

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Solution for 3x^2-28x-481=0 equation: 


Simplifying
3x2 + -28x + -481 = 0

Reorder the terms:
-481 + -28x + 3x2 = 0

Solving
-481 + -28x + 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'.
-160.3333333 + -9.333333333x + x2 = 0

Move the constant term to the right:

Add '160.3333333' to each side of the equation.
-160.3333333 + -9.333333333x + 160.3333333 + x2 = 0 + 160.3333333

Reorder the terms:
-160.3333333 + 160.3333333 + -9.333333333x + x2 = 0 + 160.3333333

Combine like terms: -160.3333333 + 160.3333333 = 0.0000000
0.0000000 + -9.333333333x + x2 = 0 + 160.3333333
-9.333333333x + x2 = 0 + 160.3333333

Combine like terms: 0 + 160.3333333 = 160.3333333
-9.333333333x + x2 = 160.3333333

The x term is -9.333333333x.  Take half its coefficient (-4.666666667).
Square it (21.77777778) and add it to both sides.

Add '21.77777778' to each side of the equation.
-9.333333333x + 21.77777778 + x2 = 160.3333333 + 21.77777778

Reorder the terms:
21.77777778 + -9.333333333x + x2 = 160.3333333 + 21.77777778

Combine like terms: 160.3333333 + 21.77777778 = 182.11111108
21.77777778 + -9.333333333x + x2 = 182.11111108

Factor a perfect square on the left side:
(x + -4.666666667)(x + -4.666666667) = 182.11111108

Calculate the square root of the right side: 13.494854986

Break this problem into two subproblems by setting 
(x + -4.666666667) equal to 13.494854986 and -13.494854986.


Subproblem 1
x + -4.666666667 = 13.494854986

Simplifying
x + -4.666666667 = 13.494854986

Reorder the terms:
-4.666666667 + x = 13.494854986

Solving
-4.666666667 + x = 13.494854986

Solving for variable 'x'.

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

Add '4.666666667' to each side of the equation.
-4.666666667 + 4.666666667 + x = 13.494854986 + 4.666666667

Combine like terms: -4.666666667 + 4.666666667 = 0.000000000
0.000000000 + x = 13.494854986 + 4.666666667
x = 13.494854986 + 4.666666667

Combine like terms: 13.494854986 + 4.666666667 = 18.161521653
x = 18.161521653

Simplifying
x = 18.161521653


Subproblem 2
x + -4.666666667 = -13.494854986

Simplifying
x + -4.666666667 = -13.494854986

Reorder the terms:
-4.666666667 + x = -13.494854986

Solving
-4.666666667 + x = -13.494854986

Solving for variable 'x'.

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

Add '4.666666667' to each side of the equation.
-4.666666667 + 4.666666667 + x = -13.494854986 + 4.666666667

Combine like terms: -4.666666667 + 4.666666667 = 0.000000000
0.000000000 + x = -13.494854986 + 4.666666667
x = -13.494854986 + 4.666666667

Combine like terms: -13.494854986 + 4.666666667 = -8.828188319
x = -8.828188319

Simplifying
x = -8.828188319


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {18.161521653, -8.828188319}

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