b^2-b-20=20

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Solution for b^2-b-20=20 equation:


Simplifying
b2 + -1b + -20 = 20

Reorder the terms:
-20 + -1b + b2 = 20

Solving
-20 + -1b + b2 = 20

Solving for variable 'b'.

Reorder the terms:
-20 + -20 + -1b + b2 = 20 + -20

Combine like terms: -20 + -20 = -40
-40 + -1b + b2 = 20 + -20

Combine like terms: 20 + -20 = 0
-40 + -1b + b2 = 0

Begin completing the square.

Move the constant term to the right:

Add '40' to each side of the equation.
-40 + -1b + 40 + b2 = 0 + 40

Reorder the terms:
-40 + 40 + -1b + b2 = 0 + 40

Combine like terms: -40 + 40 = 0
0 + -1b + b2 = 0 + 40
-1b + b2 = 0 + 40

Combine like terms: 0 + 40 = 40
-1b + b2 = 40

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 = 40 + 0.25

Reorder the terms:
0.25 + -1b + b2 = 40 + 0.25

Combine like terms: 40 + 0.25 = 40.25
0.25 + -1b + b2 = 40.25

Factor a perfect square on the left side:
(b + -0.5)(b + -0.5) = 40.25

Calculate the square root of the right side: 6.34428877

Break this problem into two subproblems by setting 
(b + -0.5) equal to 6.34428877 and -6.34428877.

Subproblem 1

b + -0.5 = 6.34428877 Simplifying b + -0.5 = 6.34428877 Reorder the terms: -0.5 + b = 6.34428877 Solving -0.5 + b = 6.34428877 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 = 6.34428877 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + b = 6.34428877 + 0.5 b = 6.34428877 + 0.5 Combine like terms: 6.34428877 + 0.5 = 6.84428877 b = 6.84428877 Simplifying b = 6.84428877

Subproblem 2

b + -0.5 = -6.34428877 Simplifying b + -0.5 = -6.34428877 Reorder the terms: -0.5 + b = -6.34428877 Solving -0.5 + b = -6.34428877 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 = -6.34428877 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + b = -6.34428877 + 0.5 b = -6.34428877 + 0.5 Combine like terms: -6.34428877 + 0.5 = -5.84428877 b = -5.84428877 Simplifying b = -5.84428877

Solution

The solution to the problem is based on the solutions from the subproblems. b = {6.84428877, -5.84428877}

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