6x^2-47x-46=0

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Solution for 6x^2-47x-46=0 equation: 


Simplifying
6x2 + -47x + -46 = 0

Reorder the terms:
-46 + -47x + 6x2 = 0

Solving
-46 + -47x + 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'.
-7.666666667 + -7.833333333x + x2 = 0

Move the constant term to the right:

Add '7.666666667' to each side of the equation.
-7.666666667 + -7.833333333x + 7.666666667 + x2 = 0 + 7.666666667

Reorder the terms:
-7.666666667 + 7.666666667 + -7.833333333x + x2 = 0 + 7.666666667

Combine like terms: -7.666666667 + 7.666666667 = 0.000000000
0.000000000 + -7.833333333x + x2 = 0 + 7.666666667
-7.833333333x + x2 = 0 + 7.666666667

Combine like terms: 0 + 7.666666667 = 7.666666667
-7.833333333x + x2 = 7.666666667

The x term is -7.833333333x.  Take half its coefficient (-3.916666667).
Square it (15.34027778) and add it to both sides.

Add '15.34027778' to each side of the equation.
-7.833333333x + 15.34027778 + x2 = 7.666666667 + 15.34027778

Reorder the terms:
15.34027778 + -7.833333333x + x2 = 7.666666667 + 15.34027778

Combine like terms: 7.666666667 + 15.34027778 = 23.006944447
15.34027778 + -7.833333333x + x2 = 23.006944447

Factor a perfect square on the left side:
(x + -3.916666667)(x + -3.916666667) = 23.006944447

Calculate the square root of the right side: 4.796555477

Break this problem into two subproblems by setting 
(x + -3.916666667) equal to 4.796555477 and -4.796555477.


Subproblem 1
x + -3.916666667 = 4.796555477

Simplifying
x + -3.916666667 = 4.796555477

Reorder the terms:
-3.916666667 + x = 4.796555477

Solving
-3.916666667 + x = 4.796555477

Solving for variable 'x'.

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

Add '3.916666667' to each side of the equation.
-3.916666667 + 3.916666667 + x = 4.796555477 + 3.916666667

Combine like terms: -3.916666667 + 3.916666667 = 0.000000000
0.000000000 + x = 4.796555477 + 3.916666667
x = 4.796555477 + 3.916666667

Combine like terms: 4.796555477 + 3.916666667 = 8.713222144
x = 8.713222144

Simplifying
x = 8.713222144


Subproblem 2
x + -3.916666667 = -4.796555477

Simplifying
x + -3.916666667 = -4.796555477

Reorder the terms:
-3.916666667 + x = -4.796555477

Solving
-3.916666667 + x = -4.796555477

Solving for variable 'x'.

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

Add '3.916666667' to each side of the equation.
-3.916666667 + 3.916666667 + x = -4.796555477 + 3.916666667

Combine like terms: -3.916666667 + 3.916666667 = 0.000000000
0.000000000 + x = -4.796555477 + 3.916666667
x = -4.796555477 + 3.916666667

Combine like terms: -4.796555477 + 3.916666667 = -0.87988881
x = -0.87988881

Simplifying
x = -0.87988881


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.713222144, -0.87988881}

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