2b^2=9b+45

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Solution for 2b^2=9b+45 equation:


Simplifying
2b2 = 9b + 45

Reorder the terms:
2b2 = 45 + 9b

Solving
2b2 = 45 + 9b

Solving for variable 'b'.

Reorder the terms:
-45 + -9b + 2b2 = 45 + 9b + -45 + -9b

Reorder the terms:
-45 + -9b + 2b2 = 45 + -45 + 9b + -9b

Combine like terms: 45 + -45 = 0
-45 + -9b + 2b2 = 0 + 9b + -9b
-45 + -9b + 2b2 = 9b + -9b

Combine like terms: 9b + -9b = 0
-45 + -9b + 2b2 = 0

Factor a trinomial.
(-3 + -1b)(15 + -2b) = 0

Subproblem 1

Set the factor '(-3 + -1b)' equal to zero and attempt to solve: Simplifying -3 + -1b = 0 Solving -3 + -1b = 0 Move all terms containing b to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1b = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1b = 0 + 3 -1b = 0 + 3 Combine like terms: 0 + 3 = 3 -1b = 3 Divide each side by '-1'. b = -3 Simplifying b = -3

Subproblem 2

Set the factor '(15 + -2b)' equal to zero and attempt to solve: Simplifying 15 + -2b = 0 Solving 15 + -2b = 0 Move all terms containing b to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + -2b = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -2b = 0 + -15 -2b = 0 + -15 Combine like terms: 0 + -15 = -15 -2b = -15 Divide each side by '-2'. b = 7.5 Simplifying b = 7.5

Solution

b = {-3, 7.5}

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