B^2+.5B=25.5

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Solution for B^2+.5B=25.5 equation: 


Simplifying
B2 + 0.5B = 25.5

Reorder the terms:
0.5B + B2 = 25.5

Solving
0.5B + B2 = 25.5

Solving for variable 'B'.

Reorder the terms:
-25.5 + 0.5B + B2 = 25.5 + -25.5

Combine like terms: 25.5 + -25.5 = 0.0
-25.5 + 0.5B + B2 = 0.0

Begin completing the square.

Move the constant term to the right:

Add '25.5' to each side of the equation.
-25.5 + 0.5B + 25.5 + B2 = 0.0 + 25.5

Reorder the terms:
-25.5 + 25.5 + 0.5B + B2 = 0.0 + 25.5

Combine like terms: -25.5 + 25.5 = 0.0
0.0 + 0.5B + B2 = 0.0 + 25.5
0.5B + B2 = 0.0 + 25.5

Combine like terms: 0.0 + 25.5 = 25.5
0.5B + B2 = 25.5

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 = 25.5 + 0.0625

Reorder the terms:
0.0625 + 0.5B + B2 = 25.5 + 0.0625

Combine like terms: 25.5 + 0.0625 = 25.5625
0.0625 + 0.5B + B2 = 25.5625

Factor a perfect square on the left side:
(B + 0.25)(B + 0.25) = 25.5625

Calculate the square root of the right side: 5.055937104

Break this problem into two subproblems by setting 
(B + 0.25) equal to 5.055937104 and -5.055937104.


Subproblem 1
B + 0.25 = 5.055937104

Simplifying
B + 0.25 = 5.055937104

Reorder the terms:
0.25 + B = 5.055937104

Solving
0.25 + B = 5.055937104

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 = 5.055937104 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + B = 5.055937104 + -0.25
B = 5.055937104 + -0.25

Combine like terms: 5.055937104 + -0.25 = 4.805937104
B = 4.805937104

Simplifying
B = 4.805937104


Subproblem 2
B + 0.25 = -5.055937104

Simplifying
B + 0.25 = -5.055937104

Reorder the terms:
0.25 + B = -5.055937104

Solving
0.25 + B = -5.055937104

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 = -5.055937104 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + B = -5.055937104 + -0.25
B = -5.055937104 + -0.25

Combine like terms: -5.055937104 + -0.25 = -5.305937104
B = -5.305937104

Simplifying
B = -5.305937104


Solution
The solution to the problem is based on the solutions
from the subproblems.
B = {4.805937104, -5.305937104}

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