6x^2+35x-84=0

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Solution for 6x^2+35x-84=0 equation: 


Simplifying
6x2 + 35x + -84 = 0

Reorder the terms:
-84 + 35x + 6x2 = 0

Solving
-84 + 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'.
-14 + 5.833333333x + x2 = 0

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + 5.833333333x + 14 + x2 = 0 + 14

Reorder the terms:
-14 + 14 + 5.833333333x + x2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + 5.833333333x + x2 = 0 + 14
5.833333333x + x2 = 0 + 14

Combine like terms: 0 + 14 = 14
5.833333333x + x2 = 14

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 = 14 + 8.506944446

Reorder the terms:
8.506944446 + 5.833333333x + x2 = 14 + 8.506944446

Combine like terms: 14 + 8.506944446 = 22.506944446
8.506944446 + 5.833333333x + x2 = 22.506944446

Factor a perfect square on the left side:
(x + 2.916666667)(x + 2.916666667) = 22.506944446

Calculate the square root of the right side: 4.744148443

Break this problem into two subproblems by setting 
(x + 2.916666667) equal to 4.744148443 and -4.744148443.


Subproblem 1
x + 2.916666667 = 4.744148443

Simplifying
x + 2.916666667 = 4.744148443

Reorder the terms:
2.916666667 + x = 4.744148443

Solving
2.916666667 + x = 4.744148443

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 = 4.744148443 + -2.916666667

Combine like terms: 2.916666667 + -2.916666667 = 0.000000000
0.000000000 + x = 4.744148443 + -2.916666667
x = 4.744148443 + -2.916666667

Combine like terms: 4.744148443 + -2.916666667 = 1.827481776
x = 1.827481776

Simplifying
x = 1.827481776


Subproblem 2
x + 2.916666667 = -4.744148443

Simplifying
x + 2.916666667 = -4.744148443

Reorder the terms:
2.916666667 + x = -4.744148443

Solving
2.916666667 + x = -4.744148443

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 = -4.744148443 + -2.916666667

Combine like terms: 2.916666667 + -2.916666667 = 0.000000000
0.000000000 + x = -4.744148443 + -2.916666667
x = -4.744148443 + -2.916666667

Combine like terms: -4.744148443 + -2.916666667 = -7.66081511
x = -7.66081511

Simplifying
x = -7.66081511


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.827481776, -7.66081511}

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