6x^2+x-16=0

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Solution for 6x^2+x-16=0 equation: 


Simplifying
6x2 + x + -16 = 0

Reorder the terms:
-16 + x + 6x2 = 0

Solving
-16 + x + 6x2 = 0

Solving for variable 'x'.

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

Divide each side by '6'.
-2.666666667 + 0.1666666667x + x2 = 0

Move the constant term to the right:

Add '2.666666667' to each side of the equation.
-2.666666667 + 0.1666666667x + 2.666666667 + x2 = 0 + 2.666666667

Reorder the terms:
-2.666666667 + 2.666666667 + 0.1666666667x + x2 = 0 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + 0.1666666667x + x2 = 0 + 2.666666667
0.1666666667x + x2 = 0 + 2.666666667

Combine like terms: 0 + 2.666666667 = 2.666666667
0.1666666667x + x2 = 2.666666667

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.1666666667x + 0.25 + x2 = 2.666666667 + 0.25

Reorder the terms:
0.25 + 0.1666666667x + x2 = 2.666666667 + 0.25

Combine like terms: 2.666666667 + 0.25 = 2.916666667
0.25 + 0.1666666667x + x2 = 2.916666667

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 2.916666667

Calculate the square root of the right side: 1.707825128

Break this problem into two subproblems by setting 
(x + 0.5) equal to 1.707825128 and -1.707825128.


Subproblem 1
x + 0.5 = 1.707825128

Simplifying
x + 0.5 = 1.707825128

Reorder the terms:
0.5 + x = 1.707825128

Solving
0.5 + x = 1.707825128

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 1.707825128 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 1.707825128 + -0.5
x = 1.707825128 + -0.5

Combine like terms: 1.707825128 + -0.5 = 1.207825128
x = 1.207825128

Simplifying
x = 1.207825128


Subproblem 2
x + 0.5 = -1.707825128

Simplifying
x + 0.5 = -1.707825128

Reorder the terms:
0.5 + x = -1.707825128

Solving
0.5 + x = -1.707825128

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -1.707825128 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -1.707825128 + -0.5
x = -1.707825128 + -0.5

Combine like terms: -1.707825128 + -0.5 = -2.207825128
x = -2.207825128

Simplifying
x = -2.207825128


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.207825128, -2.207825128}

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