8b^2-4b-30=-10

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Solution for 8b^2-4b-30=-10 equation: 


Simplifying
8b2 + -4b + -30 = -10

Reorder the terms:
-30 + -4b + 8b2 = -10

Solving
-30 + -4b + 8b2 = -10

Solving for variable 'b'.

Reorder the terms:
-30 + 10 + -4b + 8b2 = -10 + 10

Combine like terms: -30 + 10 = -20
-20 + -4b + 8b2 = -10 + 10

Combine like terms: -10 + 10 = 0
-20 + -4b + 8b2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-5 + -1b + 2b2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-5 + -1b + 2b2)' equal to zero and attempt to solve:

Simplifying
-5 + -1b + 2b2 = 0

Solving
-5 + -1b + 2b2 = 0

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

Divide each side by '2'.
-2.5 + -0.5b + b2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + -0.5b + 2.5 + b2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + -0.5b + b2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + -0.5b + b2 = 0 + 2.5
-0.5b + b2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
-0.5b + b2 = 2.5

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 = 2.5 + 0.0625

Reorder the terms:
0.0625 + -0.5b + b2 = 2.5 + 0.0625

Combine like terms: 2.5 + 0.0625 = 2.5625
0.0625 + -0.5b + b2 = 2.5625

Factor a perfect square on the left side:
(b + -0.25)(b + -0.25) = 2.5625

Calculate the square root of the right side: 1.600781059

Break this problem into two subproblems by setting 
(b + -0.25) equal to 1.600781059 and -1.600781059.


Subproblem 1
b + -0.25 = 1.600781059

Simplifying
b + -0.25 = 1.600781059

Reorder the terms:
-0.25 + b = 1.600781059

Solving
-0.25 + b = 1.600781059

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 = 1.600781059 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + b = 1.600781059 + 0.25
b = 1.600781059 + 0.25

Combine like terms: 1.600781059 + 0.25 = 1.850781059
b = 1.850781059

Simplifying
b = 1.850781059


Subproblem 2
b + -0.25 = -1.600781059

Simplifying
b + -0.25 = -1.600781059

Reorder the terms:
-0.25 + b = -1.600781059

Solving
-0.25 + b = -1.600781059

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 = -1.600781059 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + b = -1.600781059 + 0.25
b = -1.600781059 + 0.25

Combine like terms: -1.600781059 + 0.25 = -1.350781059
b = -1.350781059

Simplifying
b = -1.350781059


Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {1.850781059, -1.350781059}
Solution
b = {1.850781059, -1.350781059}

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