2v^2=9v-4

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


Simplifying
2v2 = 9v + -4

Reorder the terms:
2v2 = -4 + 9v

Solving
2v2 = -4 + 9v

Solving for variable 'v'.

Reorder the terms:
4 + -9v + 2v2 = -4 + 9v + 4 + -9v

Reorder the terms:
4 + -9v + 2v2 = -4 + 4 + 9v + -9v

Combine like terms: -4 + 4 = 0
4 + -9v + 2v2 = 0 + 9v + -9v
4 + -9v + 2v2 = 9v + -9v

Combine like terms: 9v + -9v = 0
4 + -9v + 2v2 = 0

Factor a trinomial.
(1 + -2v)(4 + -1v) = 0

Subproblem 1

Set the factor '(1 + -2v)' equal to zero and attempt to solve: Simplifying 1 + -2v = 0 Solving 1 + -2v = 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 + -2v = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2v = 0 + -1 -2v = 0 + -1 Combine like terms: 0 + -1 = -1 -2v = -1 Divide each side by '-2'. v = 0.5 Simplifying v = 0.5

Subproblem 2

Set the factor '(4 + -1v)' equal to zero and attempt to solve: Simplifying 4 + -1v = 0 Solving 4 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1v = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1v = 0 + -4 -1v = 0 + -4 Combine like terms: 0 + -4 = -4 -1v = -4 Divide each side by '-1'. v = 4 Simplifying v = 4

Solution

v = {0.5, 4}

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