2b^2+5b-62=0

Solution for 2b^2+5b-62=0 equation:

Simplifying
2b2 + 5b + -62 = 0

Reorder the terms:
-62 + 5b + 2b2 = 0

Solving
-62 + 5b + 2b2 = 0

Solving for variable 'b'.

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

Divide each side by '2'.
-31 + 2.5b + b2 = 0

Move the constant term to the right:

Add '31' to each side of the equation.
-31 + 2.5b + 31 + b2 = 0 + 31

Reorder the terms:
-31 + 31 + 2.5b + b2 = 0 + 31

Combine like terms: -31 + 31 = 0
0 + 2.5b + b2 = 0 + 31
2.5b + b2 = 0 + 31

Combine like terms: 0 + 31 = 31
2.5b + b2 = 31

The b term is 2.5b.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5b + 1.5625 + b2 = 31 + 1.5625

Reorder the terms:
1.5625 + 2.5b + b2 = 31 + 1.5625

Combine like terms: 31 + 1.5625 = 32.5625
1.5625 + 2.5b + b2 = 32.5625

Factor a perfect square on the left side:
(b + 1.25)(b + 1.25) = 32.5625

Calculate the square root of the right side: 5.706356105

Break this problem into two subproblems by setting 
(b + 1.25) equal to 5.706356105 and -5.706356105.

Subproblem 1
b + 1.25 = 5.706356105

Simplifying
b + 1.25 = 5.706356105

Reorder the terms:
1.25 + b = 5.706356105

Solving
1.25 + b = 5.706356105

Solving for variable 'b'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + b = 5.706356105 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + b = 5.706356105 + -1.25
b = 5.706356105 + -1.25

Combine like terms: 5.706356105 + -1.25 = 4.456356105
b = 4.456356105

Simplifying
b = 4.456356105

Subproblem 2
b + 1.25 = -5.706356105

Simplifying
b + 1.25 = -5.706356105

Reorder the terms:
1.25 + b = -5.706356105

Solving
1.25 + b = -5.706356105

Solving for variable 'b'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + b = -5.706356105 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + b = -5.706356105 + -1.25
b = -5.706356105 + -1.25

Combine like terms: -5.706356105 + -1.25 = -6.956356105
b = -6.956356105

Simplifying
b = -6.956356105

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {4.456356105, -6.956356105}