4v^2=9v-5

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Solution for 4v^2=9v-5 equation:


Simplifying
4v2 = 9v + -5

Reorder the terms:
4v2 = -5 + 9v

Solving
4v2 = -5 + 9v

Solving for variable 'v'.

Reorder the terms:
5 + -9v + 4v2 = -5 + 9v + 5 + -9v

Reorder the terms:
5 + -9v + 4v2 = -5 + 5 + 9v + -9v

Combine like terms: -5 + 5 = 0
5 + -9v + 4v2 = 0 + 9v + -9v
5 + -9v + 4v2 = 9v + -9v

Combine like terms: 9v + -9v = 0
5 + -9v + 4v2 = 0

Factor a trinomial.
(1 + -1v)(5 + -4v) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(5 + -4v)' equal to zero and attempt to solve: Simplifying 5 + -4v = 0 Solving 5 + -4v = 0 Move all terms containing v to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -4v = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4v = 0 + -5 -4v = 0 + -5 Combine like terms: 0 + -5 = -5 -4v = -5 Divide each side by '-4'. v = 1.25 Simplifying v = 1.25

Solution

v = {1, 1.25}

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