2b^2-b-30=0

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Solution for 2b^2-b-30=0 equation:


Simplifying
2b2 + -1b + -30 = 0

Reorder the terms:
-30 + -1b + 2b2 = 0

Solving
-30 + -1b + 2b2 = 0

Solving for variable 'b'.

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

Divide each side by '2'.
-15 + -0.5b + b2 = 0

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + -0.5b + 15 + b2 = 0 + 15

Reorder the terms:
-15 + 15 + -0.5b + b2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -0.5b + b2 = 0 + 15
-0.5b + b2 = 0 + 15

Combine like terms: 0 + 15 = 15
-0.5b + b2 = 15

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 = 15 + 0.0625

Reorder the terms:
0.0625 + -0.5b + b2 = 15 + 0.0625

Combine like terms: 15 + 0.0625 = 15.0625
0.0625 + -0.5b + b2 = 15.0625

Factor a perfect square on the left side:
(b + -0.25)(b + -0.25) = 15.0625

Calculate the square root of the right side: 3.881043674

Break this problem into two subproblems by setting 
(b + -0.25) equal to 3.881043674 and -3.881043674.

Subproblem 1

b + -0.25 = 3.881043674 Simplifying b + -0.25 = 3.881043674 Reorder the terms: -0.25 + b = 3.881043674 Solving -0.25 + b = 3.881043674 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 = 3.881043674 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + b = 3.881043674 + 0.25 b = 3.881043674 + 0.25 Combine like terms: 3.881043674 + 0.25 = 4.131043674 b = 4.131043674 Simplifying b = 4.131043674

Subproblem 2

b + -0.25 = -3.881043674 Simplifying b + -0.25 = -3.881043674 Reorder the terms: -0.25 + b = -3.881043674 Solving -0.25 + b = -3.881043674 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 = -3.881043674 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + b = -3.881043674 + 0.25 b = -3.881043674 + 0.25 Combine like terms: -3.881043674 + 0.25 = -3.631043674 b = -3.631043674 Simplifying b = -3.631043674

Solution

The solution to the problem is based on the solutions from the subproblems. b = {4.131043674, -3.631043674}

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