6x^2+97x-2=0

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Solution for 6x^2+97x-2=0 equation: 


Simplifying
6x2 + 97x + -2 = 0

Reorder the terms:
-2 + 97x + 6x2 = 0

Solving
-2 + 97x + 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'.
-0.3333333333 + 16.16666667x + x2 = 0

Move the constant term to the right:

Add '0.3333333333' to each side of the equation.
-0.3333333333 + 16.16666667x + 0.3333333333 + x2 = 0 + 0.3333333333

Reorder the terms:
-0.3333333333 + 0.3333333333 + 16.16666667x + x2 = 0 + 0.3333333333

Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000
0.0000000000 + 16.16666667x + x2 = 0 + 0.3333333333
16.16666667x + x2 = 0 + 0.3333333333

Combine like terms: 0 + 0.3333333333 = 0.3333333333
16.16666667x + x2 = 0.3333333333

The x term is 16.16666667x.  Take half its coefficient (8.083333335).
Square it (65.34027780) and add it to both sides.

Add '65.34027780' to each side of the equation.
16.16666667x + 65.34027780 + x2 = 0.3333333333 + 65.34027780

Reorder the terms:
65.34027780 + 16.16666667x + x2 = 0.3333333333 + 65.34027780

Combine like terms: 0.3333333333 + 65.34027780 = 65.6736111333
65.34027780 + 16.16666667x + x2 = 65.6736111333

Factor a perfect square on the left side:
(x + 8.083333335)(x + 8.083333335) = 65.6736111333

Calculate the square root of the right side: 8.103925662

Break this problem into two subproblems by setting 
(x + 8.083333335) equal to 8.103925662 and -8.103925662.


Subproblem 1
x + 8.083333335 = 8.103925662

Simplifying
x + 8.083333335 = 8.103925662

Reorder the terms:
8.083333335 + x = 8.103925662

Solving
8.083333335 + x = 8.103925662

Solving for variable 'x'.

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

Add '-8.083333335' to each side of the equation.
8.083333335 + -8.083333335 + x = 8.103925662 + -8.083333335

Combine like terms: 8.083333335 + -8.083333335 = 0.000000000
0.000000000 + x = 8.103925662 + -8.083333335
x = 8.103925662 + -8.083333335

Combine like terms: 8.103925662 + -8.083333335 = 0.020592327
x = 0.020592327

Simplifying
x = 0.020592327


Subproblem 2
x + 8.083333335 = -8.103925662

Simplifying
x + 8.083333335 = -8.103925662

Reorder the terms:
8.083333335 + x = -8.103925662

Solving
8.083333335 + x = -8.103925662

Solving for variable 'x'.

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

Add '-8.083333335' to each side of the equation.
8.083333335 + -8.083333335 + x = -8.103925662 + -8.083333335

Combine like terms: 8.083333335 + -8.083333335 = 0.000000000
0.000000000 + x = -8.103925662 + -8.083333335
x = -8.103925662 + -8.083333335

Combine like terms: -8.103925662 + -8.083333335 = -16.187258997
x = -16.187258997

Simplifying
x = -16.187258997


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.020592327, -16.187258997}

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