b^2+.5b=3

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Solution for b^2+.5b=3 equation:


Simplifying
b2 + 0.5b = 3

Reorder the terms:
0.5b + b2 = 3

Solving
0.5b + b2 = 3

Solving for variable 'b'.

Reorder the terms:
-3 + 0.5b + b2 = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + 0.5b + b2 = 0

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 0.5b + 3 + b2 = 0 + 3

Reorder the terms:
-3 + 3 + 0.5b + b2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 0.5b + b2 = 0 + 3
0.5b + b2 = 0 + 3

Combine like terms: 0 + 3 = 3
0.5b + b2 = 3

The b term is 0.5b.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5b + 0.0625 + b2 = 3 + 0.0625

Reorder the terms:
0.0625 + 0.5b + b2 = 3 + 0.0625

Combine like terms: 3 + 0.0625 = 3.0625
0.0625 + 0.5b + b2 = 3.0625

Factor a perfect square on the left side:
(b + 0.25)(b + 0.25) = 3.0625

Calculate the square root of the right side: 1.75

Break this problem into two subproblems by setting 
(b + 0.25) equal to 1.75 and -1.75.

Subproblem 1

b + 0.25 = 1.75 Simplifying b + 0.25 = 1.75 Reorder the terms: 0.25 + b = 1.75 Solving 0.25 + b = 1.75 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + b = 1.75 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + b = 1.75 + -0.25 b = 1.75 + -0.25 Combine like terms: 1.75 + -0.25 = 1.5 b = 1.5 Simplifying b = 1.5

Subproblem 2

b + 0.25 = -1.75 Simplifying b + 0.25 = -1.75 Reorder the terms: 0.25 + b = -1.75 Solving 0.25 + b = -1.75 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + b = -1.75 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + b = -1.75 + -0.25 b = -1.75 + -0.25 Combine like terms: -1.75 + -0.25 = -2 b = -2 Simplifying b = -2

Solution

The solution to the problem is based on the solutions from the subproblems. b = {1.5, -2}

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