5b^2-16=-38b

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Solution for 5b^2-16=-38b equation:


Simplifying
5b2 + -16 = -38b

Reorder the terms:
-16 + 5b2 = -38b

Solving
-16 + 5b2 = -38b

Solving for variable 'b'.

Reorder the terms:
-16 + 38b + 5b2 = -38b + 38b

Combine like terms: -38b + 38b = 0
-16 + 38b + 5b2 = 0

Factor a trinomial.
(-8 + -1b)(2 + -5b) = 0

Subproblem 1

Set the factor '(-8 + -1b)' equal to zero and attempt to solve: Simplifying -8 + -1b = 0 Solving -8 + -1b = 0 Move all terms containing b to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -1b = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1b = 0 + 8 -1b = 0 + 8 Combine like terms: 0 + 8 = 8 -1b = 8 Divide each side by '-1'. b = -8 Simplifying b = -8

Subproblem 2

Set the factor '(2 + -5b)' equal to zero and attempt to solve: Simplifying 2 + -5b = 0 Solving 2 + -5b = 0 Move all terms containing b to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -5b = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5b = 0 + -2 -5b = 0 + -2 Combine like terms: 0 + -2 = -2 -5b = -2 Divide each side by '-5'. b = 0.4 Simplifying b = 0.4

Solution

b = {-8, 0.4}

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