4v^2+3v-74=11

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Solution for 4v^2+3v-74=11 equation:


Simplifying
4v2 + 3v + -74 = 11

Reorder the terms:
-74 + 3v + 4v2 = 11

Solving
-74 + 3v + 4v2 = 11

Solving for variable 'v'.

Reorder the terms:
-74 + -11 + 3v + 4v2 = 11 + -11

Combine like terms: -74 + -11 = -85
-85 + 3v + 4v2 = 11 + -11

Combine like terms: 11 + -11 = 0
-85 + 3v + 4v2 = 0

Factor a trinomial.
(-5 + -1v)(17 + -4v) = 0

Subproblem 1

Set the factor '(-5 + -1v)' equal to zero and attempt to solve: Simplifying -5 + -1v = 0 Solving -5 + -1v = 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 + -1v = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1v = 0 + 5 -1v = 0 + 5 Combine like terms: 0 + 5 = 5 -1v = 5 Divide each side by '-1'. v = -5 Simplifying v = -5

Subproblem 2

Set the factor '(17 + -4v)' equal to zero and attempt to solve: Simplifying 17 + -4v = 0 Solving 17 + -4v = 0 Move all terms containing v to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + -4v = 0 + -17 Combine like terms: 17 + -17 = 0 0 + -4v = 0 + -17 -4v = 0 + -17 Combine like terms: 0 + -17 = -17 -4v = -17 Divide each side by '-4'. v = 4.25 Simplifying v = 4.25

Solution

v = {-5, 4.25}

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