b^2+8b-22=

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Solution for b^2+8b-22= equation:


Simplifying
b2 + 8b + -22 = 0

Reorder the terms:
-22 + 8b + b2 = 0

Solving
-22 + 8b + b2 = 0

Solving for variable 'b'.

Begin completing the square.

Move the constant term to the right:

Add '22' to each side of the equation.
-22 + 8b + 22 + b2 = 0 + 22

Reorder the terms:
-22 + 22 + 8b + b2 = 0 + 22

Combine like terms: -22 + 22 = 0
0 + 8b + b2 = 0 + 22
8b + b2 = 0 + 22

Combine like terms: 0 + 22 = 22
8b + b2 = 22

The b term is 8b.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8b + 16 + b2 = 22 + 16

Reorder the terms:
16 + 8b + b2 = 22 + 16

Combine like terms: 22 + 16 = 38
16 + 8b + b2 = 38

Factor a perfect square on the left side:
(b + 4)(b + 4) = 38

Calculate the square root of the right side: 6.164414003

Break this problem into two subproblems by setting 
(b + 4) equal to 6.164414003 and -6.164414003.

Subproblem 1

b + 4 = 6.164414003 Simplifying b + 4 = 6.164414003 Reorder the terms: 4 + b = 6.164414003 Solving 4 + b = 6.164414003 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + b = 6.164414003 + -4 Combine like terms: 4 + -4 = 0 0 + b = 6.164414003 + -4 b = 6.164414003 + -4 Combine like terms: 6.164414003 + -4 = 2.164414003 b = 2.164414003 Simplifying b = 2.164414003

Subproblem 2

b + 4 = -6.164414003 Simplifying b + 4 = -6.164414003 Reorder the terms: 4 + b = -6.164414003 Solving 4 + b = -6.164414003 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + b = -6.164414003 + -4 Combine like terms: 4 + -4 = 0 0 + b = -6.164414003 + -4 b = -6.164414003 + -4 Combine like terms: -6.164414003 + -4 = -10.164414003 b = -10.164414003 Simplifying b = -10.164414003

Solution

The solution to the problem is based on the solutions from the subproblems. b = {2.164414003, -10.164414003}

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