6x^2-35x-34=0

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Solution for 6x^2-35x-34=0 equation: 


Simplifying
6x2 + -35x + -34 = 0

Reorder the terms:
-34 + -35x + 6x2 = 0

Solving
-34 + -35x + 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'.
-5.666666667 + -5.833333333x + x2 = 0

Move the constant term to the right:

Add '5.666666667' to each side of the equation.
-5.666666667 + -5.833333333x + 5.666666667 + x2 = 0 + 5.666666667

Reorder the terms:
-5.666666667 + 5.666666667 + -5.833333333x + x2 = 0 + 5.666666667

Combine like terms: -5.666666667 + 5.666666667 = 0.000000000
0.000000000 + -5.833333333x + x2 = 0 + 5.666666667
-5.833333333x + x2 = 0 + 5.666666667

Combine like terms: 0 + 5.666666667 = 5.666666667
-5.833333333x + x2 = 5.666666667

The x term is -5.833333333x.  Take half its coefficient (-2.916666667).
Square it (8.506944446) and add it to both sides.

Add '8.506944446' to each side of the equation.
-5.833333333x + 8.506944446 + x2 = 5.666666667 + 8.506944446

Reorder the terms:
8.506944446 + -5.833333333x + x2 = 5.666666667 + 8.506944446

Combine like terms: 5.666666667 + 8.506944446 = 14.173611113
8.506944446 + -5.833333333x + x2 = 14.173611113

Factor a perfect square on the left side:
(x + -2.916666667)(x + -2.916666667) = 14.173611113

Calculate the square root of the right side: 3.764785666

Break this problem into two subproblems by setting 
(x + -2.916666667) equal to 3.764785666 and -3.764785666.


Subproblem 1
x + -2.916666667 = 3.764785666

Simplifying
x + -2.916666667 = 3.764785666

Reorder the terms:
-2.916666667 + x = 3.764785666

Solving
-2.916666667 + x = 3.764785666

Solving for variable 'x'.

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

Add '2.916666667' to each side of the equation.
-2.916666667 + 2.916666667 + x = 3.764785666 + 2.916666667

Combine like terms: -2.916666667 + 2.916666667 = 0.000000000
0.000000000 + x = 3.764785666 + 2.916666667
x = 3.764785666 + 2.916666667

Combine like terms: 3.764785666 + 2.916666667 = 6.681452333
x = 6.681452333

Simplifying
x = 6.681452333


Subproblem 2
x + -2.916666667 = -3.764785666

Simplifying
x + -2.916666667 = -3.764785666

Reorder the terms:
-2.916666667 + x = -3.764785666

Solving
-2.916666667 + x = -3.764785666

Solving for variable 'x'.

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

Add '2.916666667' to each side of the equation.
-2.916666667 + 2.916666667 + x = -3.764785666 + 2.916666667

Combine like terms: -2.916666667 + 2.916666667 = 0.000000000
0.000000000 + x = -3.764785666 + 2.916666667
x = -3.764785666 + 2.916666667

Combine like terms: -3.764785666 + 2.916666667 = -0.848118999
x = -0.848118999

Simplifying
x = -0.848118999


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.681452333, -0.848118999}

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