6x^2-42x-16=0

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Solution for 6x^2-42x-16=0 equation: 


Simplifying
6x2 + -42x + -16 = 0

Reorder the terms:
-16 + -42x + 6x2 = 0

Solving
-16 + -42x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-8 + -21x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-8 + -21x + 3x2)' equal to zero and attempt to solve:

Simplifying
-8 + -21x + 3x2 = 0

Solving
-8 + -21x + 3x2 = 0

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

Divide each side by '3'.
-2.666666667 + -7x + x2 = 0

Move the constant term to the right:

Add '2.666666667' to each side of the equation.
-2.666666667 + -7x + 2.666666667 + x2 = 0 + 2.666666667

Reorder the terms:
-2.666666667 + 2.666666667 + -7x + x2 = 0 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + -7x + x2 = 0 + 2.666666667
-7x + x2 = 0 + 2.666666667

Combine like terms: 0 + 2.666666667 = 2.666666667
-7x + x2 = 2.666666667

The x term is -7x.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7x + 12.25 + x2 = 2.666666667 + 12.25

Reorder the terms:
12.25 + -7x + x2 = 2.666666667 + 12.25

Combine like terms: 2.666666667 + 12.25 = 14.916666667
12.25 + -7x + x2 = 14.916666667

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 14.916666667

Calculate the square root of the right side: 3.862210075

Break this problem into two subproblems by setting 
(x + -3.5) equal to 3.862210075 and -3.862210075.


Subproblem 1
x + -3.5 = 3.862210075

Simplifying
x + -3.5 = 3.862210075

Reorder the terms:
-3.5 + x = 3.862210075

Solving
-3.5 + x = 3.862210075

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = 3.862210075 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = 3.862210075 + 3.5
x = 3.862210075 + 3.5

Combine like terms: 3.862210075 + 3.5 = 7.362210075
x = 7.362210075

Simplifying
x = 7.362210075


Subproblem 2
x + -3.5 = -3.862210075

Simplifying
x + -3.5 = -3.862210075

Reorder the terms:
-3.5 + x = -3.862210075

Solving
-3.5 + x = -3.862210075

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = -3.862210075 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = -3.862210075 + 3.5
x = -3.862210075 + 3.5

Combine like terms: -3.862210075 + 3.5 = -0.362210075
x = -0.362210075

Simplifying
x = -0.362210075


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.362210075, -0.362210075}
Solution
x = {7.362210075, -0.362210075}

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