0=b^2-15b-18819

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Solution for 0=b^2-15b-18819 equation:


Simplifying
0 = b2 + -15b + -18819

Reorder the terms:
0 = -18819 + -15b + b2

Solving
0 = -18819 + -15b + b2

Solving for variable 'b'.

Combine like terms: 0 + 18819 = 18819
18819 + 15b + -1b2 = -18819 + -15b + b2 + 18819 + 15b + -1b2

Reorder the terms:
18819 + 15b + -1b2 = -18819 + 18819 + -15b + 15b + b2 + -1b2

Combine like terms: -18819 + 18819 = 0
18819 + 15b + -1b2 = 0 + -15b + 15b + b2 + -1b2
18819 + 15b + -1b2 = -15b + 15b + b2 + -1b2

Combine like terms: -15b + 15b = 0
18819 + 15b + -1b2 = 0 + b2 + -1b2
18819 + 15b + -1b2 = b2 + -1b2

Combine like terms: b2 + -1b2 = 0
18819 + 15b + -1b2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-18819 + -15b + b2 = 0

Move the constant term to the right:

Add '18819' to each side of the equation.
-18819 + -15b + 18819 + b2 = 0 + 18819

Reorder the terms:
-18819 + 18819 + -15b + b2 = 0 + 18819

Combine like terms: -18819 + 18819 = 0
0 + -15b + b2 = 0 + 18819
-15b + b2 = 0 + 18819

Combine like terms: 0 + 18819 = 18819
-15b + b2 = 18819

The b term is -15b.  Take half its coefficient (-7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
-15b + 56.25 + b2 = 18819 + 56.25

Reorder the terms:
56.25 + -15b + b2 = 18819 + 56.25

Combine like terms: 18819 + 56.25 = 18875.25
56.25 + -15b + b2 = 18875.25

Factor a perfect square on the left side:
(b + -7.5)(b + -7.5) = 18875.25

Calculate the square root of the right side: 137.38722648

Break this problem into two subproblems by setting 
(b + -7.5) equal to 137.38722648 and -137.38722648.

Subproblem 1

b + -7.5 = 137.38722648 Simplifying b + -7.5 = 137.38722648 Reorder the terms: -7.5 + b = 137.38722648 Solving -7.5 + b = 137.38722648 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + b = 137.38722648 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + b = 137.38722648 + 7.5 b = 137.38722648 + 7.5 Combine like terms: 137.38722648 + 7.5 = 144.88722648 b = 144.88722648 Simplifying b = 144.88722648

Subproblem 2

b + -7.5 = -137.38722648 Simplifying b + -7.5 = -137.38722648 Reorder the terms: -7.5 + b = -137.38722648 Solving -7.5 + b = -137.38722648 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + b = -137.38722648 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + b = -137.38722648 + 7.5 b = -137.38722648 + 7.5 Combine like terms: -137.38722648 + 7.5 = -129.88722648 b = -129.88722648 Simplifying b = -129.88722648

Solution

The solution to the problem is based on the solutions from the subproblems. b = {144.88722648, -129.88722648}

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