5v^2=76+v

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Solution for 5v^2=76+v equation:


Simplifying
5v2 = 76 + v

Solving
5v2 = 76 + v

Solving for variable 'v'.

Reorder the terms:
-76 + -1v + 5v2 = 76 + v + -76 + -1v

Reorder the terms:
-76 + -1v + 5v2 = 76 + -76 + v + -1v

Combine like terms: 76 + -76 = 0
-76 + -1v + 5v2 = 0 + v + -1v
-76 + -1v + 5v2 = v + -1v

Combine like terms: v + -1v = 0
-76 + -1v + 5v2 = 0

Factor a trinomial.
(-19 + -5v)(4 + -1v) = 0

Subproblem 1

Set the factor '(-19 + -5v)' equal to zero and attempt to solve: Simplifying -19 + -5v = 0 Solving -19 + -5v = 0 Move all terms containing v to the left, all other terms to the right. Add '19' to each side of the equation. -19 + 19 + -5v = 0 + 19 Combine like terms: -19 + 19 = 0 0 + -5v = 0 + 19 -5v = 0 + 19 Combine like terms: 0 + 19 = 19 -5v = 19 Divide each side by '-5'. v = -3.8 Simplifying v = -3.8

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 = {-3.8, 4}

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