3x^2-4x-54=0

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Solution for 3x^2-4x-54=0 equation: 


Simplifying
3x2 + -4x + -54 = 0

Reorder the terms:
-54 + -4x + 3x2 = 0

Solving
-54 + -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'.
-18 + -1.333333333x + x2 = 0

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + -1.333333333x + 18 + x2 = 0 + 18

Reorder the terms:
-18 + 18 + -1.333333333x + x2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + -1.333333333x + x2 = 0 + 18
-1.333333333x + x2 = 0 + 18

Combine like terms: 0 + 18 = 18
-1.333333333x + x2 = 18

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 = 18 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333x + x2 = 18 + 0.4444444442

Combine like terms: 18 + 0.4444444442 = 18.4444444442
0.4444444442 + -1.333333333x + x2 = 18.4444444442

Factor a perfect square on the left side:
(x + -0.6666666665)(x + -0.6666666665) = 18.4444444442

Calculate the square root of the right side: 4.294699576

Break this problem into two subproblems by setting 
(x + -0.6666666665) equal to 4.294699576 and -4.294699576.


Subproblem 1
x + -0.6666666665 = 4.294699576

Simplifying
x + -0.6666666665 = 4.294699576

Reorder the terms:
-0.6666666665 + x = 4.294699576

Solving
-0.6666666665 + x = 4.294699576

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 = 4.294699576 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + x = 4.294699576 + 0.6666666665
x = 4.294699576 + 0.6666666665

Combine like terms: 4.294699576 + 0.6666666665 = 4.9613662425
x = 4.9613662425

Simplifying
x = 4.9613662425


Subproblem 2
x + -0.6666666665 = -4.294699576

Simplifying
x + -0.6666666665 = -4.294699576

Reorder the terms:
-0.6666666665 + x = -4.294699576

Solving
-0.6666666665 + x = -4.294699576

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 = -4.294699576 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + x = -4.294699576 + 0.6666666665
x = -4.294699576 + 0.6666666665

Combine like terms: -4.294699576 + 0.6666666665 = -3.6280329095
x = -3.6280329095

Simplifying
x = -3.6280329095


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.9613662425, -3.6280329095}

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