3x^2-9x-16=0

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Solution for 3x^2-9x-16=0 equation: 


Simplifying
3x2 + -9x + -16 = 0

Reorder the terms:
-16 + -9x + 3x2 = 0

Solving
-16 + -9x + 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'.
-5.333333333 + -3x + x2 = 0

Move the constant term to the right:

Add '5.333333333' to each side of the equation.
-5.333333333 + -3x + 5.333333333 + x2 = 0 + 5.333333333

Reorder the terms:
-5.333333333 + 5.333333333 + -3x + x2 = 0 + 5.333333333

Combine like terms: -5.333333333 + 5.333333333 = 0.000000000
0.000000000 + -3x + x2 = 0 + 5.333333333
-3x + x2 = 0 + 5.333333333

Combine like terms: 0 + 5.333333333 = 5.333333333
-3x + x2 = 5.333333333

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 5.333333333 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 5.333333333 + 2.25

Combine like terms: 5.333333333 + 2.25 = 7.583333333
2.25 + -3x + x2 = 7.583333333

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 7.583333333

Calculate the square root of the right side: 2.753785274

Break this problem into two subproblems by setting 
(x + -1.5) equal to 2.753785274 and -2.753785274.


Subproblem 1
x + -1.5 = 2.753785274

Simplifying
x + -1.5 = 2.753785274

Reorder the terms:
-1.5 + x = 2.753785274

Solving
-1.5 + x = 2.753785274

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = 2.753785274 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 2.753785274 + 1.5
x = 2.753785274 + 1.5

Combine like terms: 2.753785274 + 1.5 = 4.253785274
x = 4.253785274

Simplifying
x = 4.253785274


Subproblem 2
x + -1.5 = -2.753785274

Simplifying
x + -1.5 = -2.753785274

Reorder the terms:
-1.5 + x = -2.753785274

Solving
-1.5 + x = -2.753785274

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = -2.753785274 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -2.753785274 + 1.5
x = -2.753785274 + 1.5

Combine like terms: -2.753785274 + 1.5 = -1.253785274
x = -1.253785274

Simplifying
x = -1.253785274


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.253785274, -1.253785274}

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