0.2b^2+15b-150=0

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Solution for 0.2b^2+15b-150=0 equation:


Simplifying
0.2b2 + 15b + -150 = 0

Reorder the terms:
-150 + 15b + 0.2b2 = 0

Solving
-150 + 15b + 0.2b2 = 0

Solving for variable 'b'.

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

Divide each side by '0.2'.
-750 + 75b + b2 = 0

Move the constant term to the right:

Add '750' to each side of the equation.
-750 + 75b + 750 + b2 = 0 + 750

Reorder the terms:
-750 + 750 + 75b + b2 = 0 + 750

Combine like terms: -750 + 750 = 0
0 + 75b + b2 = 0 + 750
75b + b2 = 0 + 750

Combine like terms: 0 + 750 = 750
75b + b2 = 750

The b term is 75b.  Take half its coefficient (37.5).
Square it (1406.25) and add it to both sides.

Add '1406.25' to each side of the equation.
75b + 1406.25 + b2 = 750 + 1406.25

Reorder the terms:
1406.25 + 75b + b2 = 750 + 1406.25

Combine like terms: 750 + 1406.25 = 2156.25
1406.25 + 75b + b2 = 2156.25

Factor a perfect square on the left side:
(b + 37.5)(b + 37.5) = 2156.25

Calculate the square root of the right side: 46.435439053

Break this problem into two subproblems by setting 
(b + 37.5) equal to 46.435439053 and -46.435439053.

Subproblem 1

b + 37.5 = 46.435439053 Simplifying b + 37.5 = 46.435439053 Reorder the terms: 37.5 + b = 46.435439053 Solving 37.5 + b = 46.435439053 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-37.5' to each side of the equation. 37.5 + -37.5 + b = 46.435439053 + -37.5 Combine like terms: 37.5 + -37.5 = 0.0 0.0 + b = 46.435439053 + -37.5 b = 46.435439053 + -37.5 Combine like terms: 46.435439053 + -37.5 = 8.935439053 b = 8.935439053 Simplifying b = 8.935439053

Subproblem 2

b + 37.5 = -46.435439053 Simplifying b + 37.5 = -46.435439053 Reorder the terms: 37.5 + b = -46.435439053 Solving 37.5 + b = -46.435439053 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-37.5' to each side of the equation. 37.5 + -37.5 + b = -46.435439053 + -37.5 Combine like terms: 37.5 + -37.5 = 0.0 0.0 + b = -46.435439053 + -37.5 b = -46.435439053 + -37.5 Combine like terms: -46.435439053 + -37.5 = -83.935439053 b = -83.935439053 Simplifying b = -83.935439053

Solution

The solution to the problem is based on the solutions from the subproblems. b = {8.935439053, -83.935439053}

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