8b^2=-b+10

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Solution for 8b^2=-b+10 equation:


Simplifying
8b2 = -1b + 10

Reorder the terms:
8b2 = 10 + -1b

Solving
8b2 = 10 + -1b

Solving for variable 'b'.

Reorder the terms:
-10 + b + 8b2 = 10 + -1b + -10 + b

Reorder the terms:
-10 + b + 8b2 = 10 + -10 + -1b + b

Combine like terms: 10 + -10 = 0
-10 + b + 8b2 = 0 + -1b + b
-10 + b + 8b2 = -1b + b

Combine like terms: -1b + b = 0
-10 + b + 8b2 = 0

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

Divide each side by '8'.
-1.25 + 0.125b + b2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + 0.125b + 1.25 + b2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + 0.125b + b2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + 0.125b + b2 = 0 + 1.25
0.125b + b2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
0.125b + b2 = 1.25

The b term is b.  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.
0.125b + 0.25 + b2 = 1.25 + 0.25

Reorder the terms:
0.25 + 0.125b + b2 = 1.25 + 0.25

Combine like terms: 1.25 + 0.25 = 1.5
0.25 + 0.125b + b2 = 1.5

Factor a perfect square on the left side:
(b + 0.5)(b + 0.5) = 1.5

Calculate the square root of the right side: 1.224744871

Break this problem into two subproblems by setting 
(b + 0.5) equal to 1.224744871 and -1.224744871.

Subproblem 1

b + 0.5 = 1.224744871 Simplifying b + 0.5 = 1.224744871 Reorder the terms: 0.5 + b = 1.224744871 Solving 0.5 + b = 1.224744871 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 = 1.224744871 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + b = 1.224744871 + -0.5 b = 1.224744871 + -0.5 Combine like terms: 1.224744871 + -0.5 = 0.724744871 b = 0.724744871 Simplifying b = 0.724744871

Subproblem 2

b + 0.5 = -1.224744871 Simplifying b + 0.5 = -1.224744871 Reorder the terms: 0.5 + b = -1.224744871 Solving 0.5 + b = -1.224744871 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 = -1.224744871 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + b = -1.224744871 + -0.5 b = -1.224744871 + -0.5 Combine like terms: -1.224744871 + -0.5 = -1.724744871 b = -1.724744871 Simplifying b = -1.724744871

Solution

The solution to the problem is based on the solutions from the subproblems. b = {0.724744871, -1.724744871}

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