3x^2-2x-663=0

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Solution for 3x^2-2x-663=0 equation: 


Simplifying
3x2 + -2x + -663 = 0

Reorder the terms:
-663 + -2x + 3x2 = 0

Solving
-663 + -2x + 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'.
-221 + -0.6666666667x + x2 = 0

Move the constant term to the right:

Add '221' to each side of the equation.
-221 + -0.6666666667x + 221 + x2 = 0 + 221

Reorder the terms:
-221 + 221 + -0.6666666667x + x2 = 0 + 221

Combine like terms: -221 + 221 = 0
0 + -0.6666666667x + x2 = 0 + 221
-0.6666666667x + x2 = 0 + 221

Combine like terms: 0 + 221 = 221
-0.6666666667x + x2 = 221

The x term is -0.6666666667x.  Take half its coefficient (-0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
-0.6666666667x + 0.1111111112 + x2 = 221 + 0.1111111112

Reorder the terms:
0.1111111112 + -0.6666666667x + x2 = 221 + 0.1111111112

Combine like terms: 221 + 0.1111111112 = 221.1111111112
0.1111111112 + -0.6666666667x + x2 = 221.1111111112

Factor a perfect square on the left side:
(x + -0.3333333334)(x + -0.3333333334) = 221.1111111112

Calculate the square root of the right side: 14.869805349

Break this problem into two subproblems by setting 
(x + -0.3333333334) equal to 14.869805349 and -14.869805349.


Subproblem 1
x + -0.3333333334 = 14.869805349

Simplifying
x + -0.3333333334 = 14.869805349

Reorder the terms:
-0.3333333334 + x = 14.869805349

Solving
-0.3333333334 + x = 14.869805349

Solving for variable 'x'.

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

Add '0.3333333334' to each side of the equation.
-0.3333333334 + 0.3333333334 + x = 14.869805349 + 0.3333333334

Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000
0.0000000000 + x = 14.869805349 + 0.3333333334
x = 14.869805349 + 0.3333333334

Combine like terms: 14.869805349 + 0.3333333334 = 15.2031386824
x = 15.2031386824

Simplifying
x = 15.2031386824


Subproblem 2
x + -0.3333333334 = -14.869805349

Simplifying
x + -0.3333333334 = -14.869805349

Reorder the terms:
-0.3333333334 + x = -14.869805349

Solving
-0.3333333334 + x = -14.869805349

Solving for variable 'x'.

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

Add '0.3333333334' to each side of the equation.
-0.3333333334 + 0.3333333334 + x = -14.869805349 + 0.3333333334

Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000
0.0000000000 + x = -14.869805349 + 0.3333333334
x = -14.869805349 + 0.3333333334

Combine like terms: -14.869805349 + 0.3333333334 = -14.5364720156
x = -14.5364720156

Simplifying
x = -14.5364720156


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.2031386824, -14.5364720156}

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