b^2+4b+4=15

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Solution for b^2+4b+4=15 equation:


Simplifying
b2 + 4b + 4 = 15

Reorder the terms:
4 + 4b + b2 = 15

Solving
4 + 4b + b2 = 15

Solving for variable 'b'.

Reorder the terms:
4 + -15 + 4b + b2 = 15 + -15

Combine like terms: 4 + -15 = -11
-11 + 4b + b2 = 15 + -15

Combine like terms: 15 + -15 = 0
-11 + 4b + b2 = 0

Begin completing the square.

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + 4b + 11 + b2 = 0 + 11

Reorder the terms:
-11 + 11 + 4b + b2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + 4b + b2 = 0 + 11
4b + b2 = 0 + 11

Combine like terms: 0 + 11 = 11
4b + b2 = 11

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 = 11 + 4

Reorder the terms:
4 + 4b + b2 = 11 + 4

Combine like terms: 11 + 4 = 15
4 + 4b + b2 = 15

Factor a perfect square on the left side:
(b + 2)(b + 2) = 15

Calculate the square root of the right side: 3.872983346

Break this problem into two subproblems by setting 
(b + 2) equal to 3.872983346 and -3.872983346.

Subproblem 1

b + 2 = 3.872983346 Simplifying b + 2 = 3.872983346 Reorder the terms: 2 + b = 3.872983346 Solving 2 + b = 3.872983346 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 = 3.872983346 + -2 Combine like terms: 2 + -2 = 0 0 + b = 3.872983346 + -2 b = 3.872983346 + -2 Combine like terms: 3.872983346 + -2 = 1.872983346 b = 1.872983346 Simplifying b = 1.872983346

Subproblem 2

b + 2 = -3.872983346 Simplifying b + 2 = -3.872983346 Reorder the terms: 2 + b = -3.872983346 Solving 2 + b = -3.872983346 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 = -3.872983346 + -2 Combine like terms: 2 + -2 = 0 0 + b = -3.872983346 + -2 b = -3.872983346 + -2 Combine like terms: -3.872983346 + -2 = -5.872983346 b = -5.872983346 Simplifying b = -5.872983346

Solution

The solution to the problem is based on the solutions from the subproblems. b = {1.872983346, -5.872983346}

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