3x^2+64x-484=0

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Solution for 3x^2+64x-484=0 equation: 


Simplifying
3x2 + 64x + -484 = 0

Reorder the terms:
-484 + 64x + 3x2 = 0

Solving
-484 + 64x + 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'.
-161.3333333 + 21.33333333x + x2 = 0

Move the constant term to the right:

Add '161.3333333' to each side of the equation.
-161.3333333 + 21.33333333x + 161.3333333 + x2 = 0 + 161.3333333

Reorder the terms:
-161.3333333 + 161.3333333 + 21.33333333x + x2 = 0 + 161.3333333

Combine like terms: -161.3333333 + 161.3333333 = 0.0000000
0.0000000 + 21.33333333x + x2 = 0 + 161.3333333
21.33333333x + x2 = 0 + 161.3333333

Combine like terms: 0 + 161.3333333 = 161.3333333
21.33333333x + x2 = 161.3333333

The x term is 21.33333333x.  Take half its coefficient (10.66666667).
Square it (113.7777778) and add it to both sides.

Add '113.7777778' to each side of the equation.
21.33333333x + 113.7777778 + x2 = 161.3333333 + 113.7777778

Reorder the terms:
113.7777778 + 21.33333333x + x2 = 161.3333333 + 113.7777778

Combine like terms: 161.3333333 + 113.7777778 = 275.1111111
113.7777778 + 21.33333333x + x2 = 275.1111111

Factor a perfect square on the left side:
(x + 10.66666667)(x + 10.66666667) = 275.1111111

Calculate the square root of the right side: 16.586473739

Break this problem into two subproblems by setting 
(x + 10.66666667) equal to 16.586473739 and -16.586473739.


Subproblem 1
x + 10.66666667 = 16.586473739

Simplifying
x + 10.66666667 = 16.586473739

Reorder the terms:
10.66666667 + x = 16.586473739

Solving
10.66666667 + x = 16.586473739

Solving for variable 'x'.

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

Add '-10.66666667' to each side of the equation.
10.66666667 + -10.66666667 + x = 16.586473739 + -10.66666667

Combine like terms: 10.66666667 + -10.66666667 = 0.00000000
0.00000000 + x = 16.586473739 + -10.66666667
x = 16.586473739 + -10.66666667

Combine like terms: 16.586473739 + -10.66666667 = 5.919807069
x = 5.919807069

Simplifying
x = 5.919807069


Subproblem 2
x + 10.66666667 = -16.586473739

Simplifying
x + 10.66666667 = -16.586473739

Reorder the terms:
10.66666667 + x = -16.586473739

Solving
10.66666667 + x = -16.586473739

Solving for variable 'x'.

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

Add '-10.66666667' to each side of the equation.
10.66666667 + -10.66666667 + x = -16.586473739 + -10.66666667

Combine like terms: 10.66666667 + -10.66666667 = 0.00000000
0.00000000 + x = -16.586473739 + -10.66666667
x = -16.586473739 + -10.66666667

Combine like terms: -16.586473739 + -10.66666667 = -27.253140409
x = -27.253140409

Simplifying
x = -27.253140409


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.919807069, -27.253140409}

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