6b^2+24b-17=0

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Solution for 6b^2+24b-17=0 equation: 


Simplifying
6b2 + 24b + -17 = 0

Reorder the terms:
-17 + 24b + 6b2 = 0

Solving
-17 + 24b + 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 + 4b + b2 = 0

Move the constant term to the right:

Add '2.833333333' to each side of the equation.
-2.833333333 + 4b + 2.833333333 + b2 = 0 + 2.833333333

Reorder the terms:
-2.833333333 + 2.833333333 + 4b + b2 = 0 + 2.833333333

Combine like terms: -2.833333333 + 2.833333333 = 0.000000000
0.000000000 + 4b + b2 = 0 + 2.833333333
4b + b2 = 0 + 2.833333333

Combine like terms: 0 + 2.833333333 = 2.833333333
4b + b2 = 2.833333333

The b term is 4b.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4b + 4 + b2 = 2.833333333 + 4

Reorder the terms:
4 + 4b + b2 = 2.833333333 + 4

Combine like terms: 2.833333333 + 4 = 6.833333333
4 + 4b + b2 = 6.833333333

Factor a perfect square on the left side:
(b + 2)(b + 2) = 6.833333333

Calculate the square root of the right side: 2.614064523

Break this problem into two subproblems by setting 
(b + 2) equal to 2.614064523 and -2.614064523.


Subproblem 1
b + 2 = 2.614064523

Simplifying
b + 2 = 2.614064523

Reorder the terms:
2 + b = 2.614064523

Solving
2 + b = 2.614064523

Solving for variable 'b'.

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

Add '-2' to each side of the equation.
2 + -2 + b = 2.614064523 + -2

Combine like terms: 2 + -2 = 0
0 + b = 2.614064523 + -2
b = 2.614064523 + -2

Combine like terms: 2.614064523 + -2 = 0.614064523
b = 0.614064523

Simplifying
b = 0.614064523


Subproblem 2
b + 2 = -2.614064523

Simplifying
b + 2 = -2.614064523

Reorder the terms:
2 + b = -2.614064523

Solving
2 + b = -2.614064523

Solving for variable 'b'.

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

Add '-2' to each side of the equation.
2 + -2 + b = -2.614064523 + -2

Combine like terms: 2 + -2 = 0
0 + b = -2.614064523 + -2
b = -2.614064523 + -2

Combine like terms: -2.614064523 + -2 = -4.614064523
b = -4.614064523

Simplifying
b = -4.614064523


Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {0.614064523, -4.614064523}

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