24b^2+8b+40=

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Solution for 24b^2+8b+40= equation: 


Simplifying
24b2 + 8b + 40 = 0

Reorder the terms:
40 + 8b + 24b2 = 0

Solving
40 + 8b + 24b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '8'.
8(5 + b + 3b2) = 0

Ignore the factor 8.

Subproblem 1
Set the factor '(5 + b + 3b2)' equal to zero and attempt to solve:

Simplifying
5 + b + 3b2 = 0

Solving
5 + b + 3b2 = 0

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

Divide each side by '3'.
1.666666667 + 0.3333333333b + b2 = 0

Move the constant term to the right:

Add '-1.666666667' to each side of the equation.
1.666666667 + 0.3333333333b + -1.666666667 + b2 = 0 + -1.666666667

Reorder the terms:
1.666666667 + -1.666666667 + 0.3333333333b + b2 = 0 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + 0.3333333333b + b2 = 0 + -1.666666667
0.3333333333b + b2 = 0 + -1.666666667

Combine like terms: 0 + -1.666666667 = -1.666666667
0.3333333333b + b2 = -1.666666667

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.
0.3333333333b + 0.25 + b2 = -1.666666667 + 0.25

Reorder the terms:
0.25 + 0.3333333333b + b2 = -1.666666667 + 0.25

Combine like terms: -1.666666667 + 0.25 = -1.416666667
0.25 + 0.3333333333b + b2 = -1.416666667

Factor a perfect square on the left side:
(b + 0.5)(b + 0.5) = -1.416666667

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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