4b^2+8b-42=7

Solution for 4b^2+8b-42=7 equation:

Simplifying
4b2 + 8b + -42 = 7

Reorder the terms:
-42 + 8b + 4b2 = 7

Solving
-42 + 8b + 4b2 = 7

Solving for variable 'b'.

Reorder the terms:
-42 + -7 + 8b + 4b2 = 7 + -7

Combine like terms: -42 + -7 = -49
-49 + 8b + 4b2 = 7 + -7

Combine like terms: 7 + -7 = 0
-49 + 8b + 4b2 = 0

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

Divide each side by '4'.
-12.25 + 2b + b2 = 0

Move the constant term to the right:

Add '12.25' to each side of the equation.
-12.25 + 2b + 12.25 + b2 = 0 + 12.25

Reorder the terms:
-12.25 + 12.25 + 2b + b2 = 0 + 12.25

Combine like terms: -12.25 + 12.25 = 0.00
0.00 + 2b + b2 = 0 + 12.25
2b + b2 = 0 + 12.25

Combine like terms: 0 + 12.25 = 12.25
2b + b2 = 12.25

The b term is 2b.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2b + 1 + b2 = 12.25 + 1

Reorder the terms:
1 + 2b + b2 = 12.25 + 1

Combine like terms: 12.25 + 1 = 13.25
1 + 2b + b2 = 13.25

Factor a perfect square on the left side:
(b + 1)(b + 1) = 13.25

Calculate the square root of the right side: 3.640054945

Break this problem into two subproblems by setting 
(b + 1) equal to 3.640054945 and -3.640054945.

Subproblem 1
b + 1 = 3.640054945

Simplifying
b + 1 = 3.640054945

Reorder the terms:
1 + b = 3.640054945

Solving
1 + b = 3.640054945

Solving for variable 'b'.

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

Add '-1' to each side of the equation.
1 + -1 + b = 3.640054945 + -1

Combine like terms: 1 + -1 = 0
0 + b = 3.640054945 + -1
b = 3.640054945 + -1

Combine like terms: 3.640054945 + -1 = 2.640054945
b = 2.640054945

Simplifying
b = 2.640054945

Subproblem 2
b + 1 = -3.640054945

Simplifying
b + 1 = -3.640054945

Reorder the terms:
1 + b = -3.640054945

Solving
1 + b = -3.640054945

Solving for variable 'b'.

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

Add '-1' to each side of the equation.
1 + -1 + b = -3.640054945 + -1

Combine like terms: 1 + -1 = 0
0 + b = -3.640054945 + -1
b = -3.640054945 + -1

Combine like terms: -3.640054945 + -1 = -4.640054945
b = -4.640054945

Simplifying
b = -4.640054945

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {2.640054945, -4.640054945}