3(x^2)-4x-69=0

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Solution for 3(x^2)-4x-69=0 equation: 


Simplifying
3(x2) + -4x + -69 = 0

Reorder the terms:
-69 + -4x + 3x2 = 0

Solving
-69 + -4x + 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'.
-23 + -1.333333333x + x2 = 0

Move the constant term to the right:

Add '23' to each side of the equation.
-23 + -1.333333333x + 23 + x2 = 0 + 23

Reorder the terms:
-23 + 23 + -1.333333333x + x2 = 0 + 23

Combine like terms: -23 + 23 = 0
0 + -1.333333333x + x2 = 0 + 23
-1.333333333x + x2 = 0 + 23

Combine like terms: 0 + 23 = 23
-1.333333333x + x2 = 23

The x term is -1.333333333x.  Take half its coefficient (-0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
-1.333333333x + 0.4444444442 + x2 = 23 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333x + x2 = 23 + 0.4444444442

Combine like terms: 23 + 0.4444444442 = 23.4444444442
0.4444444442 + -1.333333333x + x2 = 23.4444444442

Factor a perfect square on the left side:
(x + -0.6666666665)(x + -0.6666666665) = 23.4444444442

Calculate the square root of the right side: 4.841946349

Break this problem into two subproblems by setting 
(x + -0.6666666665) equal to 4.841946349 and -4.841946349.


Subproblem 1
x + -0.6666666665 = 4.841946349

Simplifying
x + -0.6666666665 = 4.841946349

Reorder the terms:
-0.6666666665 + x = 4.841946349

Solving
-0.6666666665 + x = 4.841946349

Solving for variable 'x'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + x = 4.841946349 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + x = 4.841946349 + 0.6666666665
x = 4.841946349 + 0.6666666665

Combine like terms: 4.841946349 + 0.6666666665 = 5.5086130155
x = 5.5086130155

Simplifying
x = 5.5086130155


Subproblem 2
x + -0.6666666665 = -4.841946349

Simplifying
x + -0.6666666665 = -4.841946349

Reorder the terms:
-0.6666666665 + x = -4.841946349

Solving
-0.6666666665 + x = -4.841946349

Solving for variable 'x'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + x = -4.841946349 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + x = -4.841946349 + 0.6666666665
x = -4.841946349 + 0.6666666665

Combine like terms: -4.841946349 + 0.6666666665 = -4.1752796825
x = -4.1752796825

Simplifying
x = -4.1752796825


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.5086130155, -4.1752796825}

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