b^2+5b=28

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Solution for b^2+5b=28 equation:


Simplifying
b2 + 5b = 28

Reorder the terms:
5b + b2 = 28

Solving
5b + b2 = 28

Solving for variable 'b'.

Reorder the terms:
-28 + 5b + b2 = 28 + -28

Combine like terms: 28 + -28 = 0
-28 + 5b + b2 = 0

Begin completing the square.

Move the constant term to the right:

Add '28' to each side of the equation.
-28 + 5b + 28 + b2 = 0 + 28

Reorder the terms:
-28 + 28 + 5b + b2 = 0 + 28

Combine like terms: -28 + 28 = 0
0 + 5b + b2 = 0 + 28
5b + b2 = 0 + 28

Combine like terms: 0 + 28 = 28
5b + b2 = 28

The b term is 5b.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5b + 6.25 + b2 = 28 + 6.25

Reorder the terms:
6.25 + 5b + b2 = 28 + 6.25

Combine like terms: 28 + 6.25 = 34.25
6.25 + 5b + b2 = 34.25

Factor a perfect square on the left side:
(b + 2.5)(b + 2.5) = 34.25

Calculate the square root of the right side: 5.852349955

Break this problem into two subproblems by setting 
(b + 2.5) equal to 5.852349955 and -5.852349955.

Subproblem 1

b + 2.5 = 5.852349955 Simplifying b + 2.5 = 5.852349955 Reorder the terms: 2.5 + b = 5.852349955 Solving 2.5 + b = 5.852349955 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + b = 5.852349955 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + b = 5.852349955 + -2.5 b = 5.852349955 + -2.5 Combine like terms: 5.852349955 + -2.5 = 3.352349955 b = 3.352349955 Simplifying b = 3.352349955

Subproblem 2

b + 2.5 = -5.852349955 Simplifying b + 2.5 = -5.852349955 Reorder the terms: 2.5 + b = -5.852349955 Solving 2.5 + b = -5.852349955 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + b = -5.852349955 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + b = -5.852349955 + -2.5 b = -5.852349955 + -2.5 Combine like terms: -5.852349955 + -2.5 = -8.352349955 b = -8.352349955 Simplifying b = -8.352349955

Solution

The solution to the problem is based on the solutions from the subproblems. b = {3.352349955, -8.352349955}

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