2b^2-2b-5=0

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Solution for 2b^2-2b-5=0 equation:


Simplifying
2b2 + -2b + -5 = 0

Reorder the terms:
-5 + -2b + 2b2 = 0

Solving
-5 + -2b + 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'.
-2.5 + -1b + b2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + -1b + 2.5 + b2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + -1b + b2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + -1b + b2 = 0 + 2.5
-1b + b2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
-1b + b2 = 2.5

The b term is -1b.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1b + 0.25 + b2 = 2.5 + 0.25

Reorder the terms:
0.25 + -1b + b2 = 2.5 + 0.25

Combine like terms: 2.5 + 0.25 = 2.75
0.25 + -1b + b2 = 2.75

Factor a perfect square on the left side:
(b + -0.5)(b + -0.5) = 2.75

Calculate the square root of the right side: 1.658312395

Break this problem into two subproblems by setting 
(b + -0.5) equal to 1.658312395 and -1.658312395.

Subproblem 1

b + -0.5 = 1.658312395 Simplifying b + -0.5 = 1.658312395 Reorder the terms: -0.5 + b = 1.658312395 Solving -0.5 + b = 1.658312395 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + b = 1.658312395 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + b = 1.658312395 + 0.5 b = 1.658312395 + 0.5 Combine like terms: 1.658312395 + 0.5 = 2.158312395 b = 2.158312395 Simplifying b = 2.158312395

Subproblem 2

b + -0.5 = -1.658312395 Simplifying b + -0.5 = -1.658312395 Reorder the terms: -0.5 + b = -1.658312395 Solving -0.5 + b = -1.658312395 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + b = -1.658312395 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + b = -1.658312395 + 0.5 b = -1.658312395 + 0.5 Combine like terms: -1.658312395 + 0.5 = -1.158312395 b = -1.158312395 Simplifying b = -1.158312395

Solution

The solution to the problem is based on the solutions from the subproblems. b = {2.158312395, -1.158312395}

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