6b^2-b-17=0

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Solution for 6b^2-b-17=0 equation: 


Simplifying
6b2 + -1b + -17 = 0

Reorder the terms:
-17 + -1b + 6b2 = 0

Solving
-17 + -1b + 6b2 = 0

Solving for variable 'b'.

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

Divide each side by '6'.
-2.833333333 + -0.1666666667b + b2 = 0

Move the constant term to the right:

Add '2.833333333' to each side of the equation.
-2.833333333 + -0.1666666667b + 2.833333333 + b2 = 0 + 2.833333333

Reorder the terms:
-2.833333333 + 2.833333333 + -0.1666666667b + b2 = 0 + 2.833333333

Combine like terms: -2.833333333 + 2.833333333 = 0.000000000
0.000000000 + -0.1666666667b + b2 = 0 + 2.833333333
-0.1666666667b + b2 = 0 + 2.833333333

Combine like terms: 0 + 2.833333333 = 2.833333333
-0.1666666667b + b2 = 2.833333333

The b term is -0.1666666667b.  Take half its coefficient (-0.08333333335).
Square it (0.006944444447) and add it to both sides.

Add '0.006944444447' to each side of the equation.
-0.1666666667b + 0.006944444447 + b2 = 2.833333333 + 0.006944444447

Reorder the terms:
0.006944444447 + -0.1666666667b + b2 = 2.833333333 + 0.006944444447

Combine like terms: 2.833333333 + 0.006944444447 = 2.840277777447
0.006944444447 + -0.1666666667b + b2 = 2.840277777447

Factor a perfect square on the left side:
(b + -0.08333333335)(b + -0.08333333335) = 2.840277777447

Calculate the square root of the right side: 1.685312368

Break this problem into two subproblems by setting 
(b + -0.08333333335) equal to 1.685312368 and -1.685312368.


Subproblem 1
b + -0.08333333335 = 1.685312368

Simplifying
b + -0.08333333335 = 1.685312368

Reorder the terms:
-0.08333333335 + b = 1.685312368

Solving
-0.08333333335 + b = 1.685312368

Solving for variable 'b'.

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

Add '0.08333333335' to each side of the equation.
-0.08333333335 + 0.08333333335 + b = 1.685312368 + 0.08333333335

Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000
0.00000000000 + b = 1.685312368 + 0.08333333335
b = 1.685312368 + 0.08333333335

Combine like terms: 1.685312368 + 0.08333333335 = 1.76864570135
b = 1.76864570135

Simplifying
b = 1.76864570135


Subproblem 2
b + -0.08333333335 = -1.685312368

Simplifying
b + -0.08333333335 = -1.685312368

Reorder the terms:
-0.08333333335 + b = -1.685312368

Solving
-0.08333333335 + b = -1.685312368

Solving for variable 'b'.

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

Add '0.08333333335' to each side of the equation.
-0.08333333335 + 0.08333333335 + b = -1.685312368 + 0.08333333335

Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000
0.00000000000 + b = -1.685312368 + 0.08333333335
b = -1.685312368 + 0.08333333335

Combine like terms: -1.685312368 + 0.08333333335 = -1.60197903465
b = -1.60197903465

Simplifying
b = -1.60197903465


Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {1.76864570135, -1.60197903465}

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