7b^2+36b-39=0

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Solution for 7b^2+36b-39=0 equation: 


Simplifying
7b2 + 36b + -39 = 0

Reorder the terms:
-39 + 36b + 7b2 = 0

Solving
-39 + 36b + 7b2 = 0

Solving for variable 'b'.

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

Divide each side by '7'.
-5.571428571 + 5.142857143b + b2 = 0

Move the constant term to the right:

Add '5.571428571' to each side of the equation.
-5.571428571 + 5.142857143b + 5.571428571 + b2 = 0 + 5.571428571

Reorder the terms:
-5.571428571 + 5.571428571 + 5.142857143b + b2 = 0 + 5.571428571

Combine like terms: -5.571428571 + 5.571428571 = 0.000000000
0.000000000 + 5.142857143b + b2 = 0 + 5.571428571
5.142857143b + b2 = 0 + 5.571428571

Combine like terms: 0 + 5.571428571 = 5.571428571
5.142857143b + b2 = 5.571428571

The b term is 5.142857143b.  Take half its coefficient (2.571428572).
Square it (6.612244901) and add it to both sides.

Add '6.612244901' to each side of the equation.
5.142857143b + 6.612244901 + b2 = 5.571428571 + 6.612244901

Reorder the terms:
6.612244901 + 5.142857143b + b2 = 5.571428571 + 6.612244901

Combine like terms: 5.571428571 + 6.612244901 = 12.183673472
6.612244901 + 5.142857143b + b2 = 12.183673472

Factor a perfect square on the left side:
(b + 2.571428572)(b + 2.571428572) = 12.183673472

Calculate the square root of the right side: 3.490511921

Break this problem into two subproblems by setting 
(b + 2.571428572) equal to 3.490511921 and -3.490511921.


Subproblem 1
b + 2.571428572 = 3.490511921

Simplifying
b + 2.571428572 = 3.490511921

Reorder the terms:
2.571428572 + b = 3.490511921

Solving
2.571428572 + b = 3.490511921

Solving for variable 'b'.

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

Add '-2.571428572' to each side of the equation.
2.571428572 + -2.571428572 + b = 3.490511921 + -2.571428572

Combine like terms: 2.571428572 + -2.571428572 = 0.000000000
0.000000000 + b = 3.490511921 + -2.571428572
b = 3.490511921 + -2.571428572

Combine like terms: 3.490511921 + -2.571428572 = 0.919083349
b = 0.919083349

Simplifying
b = 0.919083349


Subproblem 2
b + 2.571428572 = -3.490511921

Simplifying
b + 2.571428572 = -3.490511921

Reorder the terms:
2.571428572 + b = -3.490511921

Solving
2.571428572 + b = -3.490511921

Solving for variable 'b'.

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

Add '-2.571428572' to each side of the equation.
2.571428572 + -2.571428572 + b = -3.490511921 + -2.571428572

Combine like terms: 2.571428572 + -2.571428572 = 0.000000000
0.000000000 + b = -3.490511921 + -2.571428572
b = -3.490511921 + -2.571428572

Combine like terms: -3.490511921 + -2.571428572 = -6.061940493
b = -6.061940493

Simplifying
b = -6.061940493


Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {0.919083349, -6.061940493}

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