9x^2-3x-16=0

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


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

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

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

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
9 the coefficient of the squared term: 

Divide each side by '9'.
-1.777777778 + -0.3333333333x + x2 = 0

Move the constant term to the right:

Add '1.777777778' to each side of the equation.
-1.777777778 + -0.3333333333x + 1.777777778 + x2 = 0 + 1.777777778

Reorder the terms:
-1.777777778 + 1.777777778 + -0.3333333333x + x2 = 0 + 1.777777778

Combine like terms: -1.777777778 + 1.777777778 = 0.000000000
0.000000000 + -0.3333333333x + x2 = 0 + 1.777777778
-0.3333333333x + x2 = 0 + 1.777777778

Combine like terms: 0 + 1.777777778 = 1.777777778
-0.3333333333x + x2 = 1.777777778

The x term is -0.3333333333x.  Take half its coefficient (-0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
-0.3333333333x + 0.02777777779 + x2 = 1.777777778 + 0.02777777779

Reorder the terms:
0.02777777779 + -0.3333333333x + x2 = 1.777777778 + 0.02777777779

Combine like terms: 1.777777778 + 0.02777777779 = 1.80555555579
0.02777777779 + -0.3333333333x + x2 = 1.80555555579

Factor a perfect square on the left side:
(x + -0.1666666667)(x + -0.1666666667) = 1.80555555579

Calculate the square root of the right side: 1.343709625

Break this problem into two subproblems by setting 
(x + -0.1666666667) equal to 1.343709625 and -1.343709625.


Subproblem 1
x + -0.1666666667 = 1.343709625

Simplifying
x + -0.1666666667 = 1.343709625

Reorder the terms:
-0.1666666667 + x = 1.343709625

Solving
-0.1666666667 + x = 1.343709625

Solving for variable 'x'.

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

Add '0.1666666667' to each side of the equation.
-0.1666666667 + 0.1666666667 + x = 1.343709625 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + x = 1.343709625 + 0.1666666667
x = 1.343709625 + 0.1666666667

Combine like terms: 1.343709625 + 0.1666666667 = 1.5103762917
x = 1.5103762917

Simplifying
x = 1.5103762917


Subproblem 2
x + -0.1666666667 = -1.343709625

Simplifying
x + -0.1666666667 = -1.343709625

Reorder the terms:
-0.1666666667 + x = -1.343709625

Solving
-0.1666666667 + x = -1.343709625

Solving for variable 'x'.

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

Add '0.1666666667' to each side of the equation.
-0.1666666667 + 0.1666666667 + x = -1.343709625 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + x = -1.343709625 + 0.1666666667
x = -1.343709625 + 0.1666666667

Combine like terms: -1.343709625 + 0.1666666667 = -1.1770429583
x = -1.1770429583

Simplifying
x = -1.1770429583


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.5103762917, -1.1770429583}

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