0=-v^2+2v+8

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Solution for 0=-v^2+2v+8 equation:


Simplifying
0 = -1v2 + 2v + 8

Reorder the terms:
0 = 8 + 2v + -1v2

Solving
0 = 8 + 2v + -1v2

Solving for variable 'v'.

Combine like terms: 0 + -8 = -8
-8 + -2v + v2 = 8 + 2v + -1v2 + -8 + -2v + v2

Reorder the terms:
-8 + -2v + v2 = 8 + -8 + 2v + -2v + -1v2 + v2

Combine like terms: 8 + -8 = 0
-8 + -2v + v2 = 0 + 2v + -2v + -1v2 + v2
-8 + -2v + v2 = 2v + -2v + -1v2 + v2

Combine like terms: 2v + -2v = 0
-8 + -2v + v2 = 0 + -1v2 + v2
-8 + -2v + v2 = -1v2 + v2

Combine like terms: -1v2 + v2 = 0
-8 + -2v + v2 = 0

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

Subproblem 1

Set the factor '(-2 + -1v)' equal to zero and attempt to solve: Simplifying -2 + -1v = 0 Solving -2 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1v = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1v = 0 + 2 -1v = 0 + 2 Combine like terms: 0 + 2 = 2 -1v = 2 Divide each side by '-1'. v = -2 Simplifying v = -2

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 = {-2, 4}

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