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Simplifying v2 + -6v + 9 = -1v + 45 Reorder the terms: 9 + -6v + v2 = -1v + 45 Reorder the terms: 9 + -6v + v2 = 45 + -1v Solving 9 + -6v + v2 = 45 + -1v Solving for variable 'v'. Reorder the terms: 9 + -45 + -6v + v + v2 = 45 + -1v + -45 + v Combine like terms: 9 + -45 = -36 -36 + -6v + v + v2 = 45 + -1v + -45 + v Combine like terms: -6v + v = -5v -36 + -5v + v2 = 45 + -1v + -45 + v Reorder the terms: -36 + -5v + v2 = 45 + -45 + -1v + v Combine like terms: 45 + -45 = 0 -36 + -5v + v2 = 0 + -1v + v -36 + -5v + v2 = -1v + v Combine like terms: -1v + v = 0 -36 + -5v + v2 = 0 Factor a trinomial. (-4 + -1v)(9 + -1v) = 0Subproblem 1
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 = -4Subproblem 2
Set the factor '(9 + -1v)' equal to zero and attempt to solve: Simplifying 9 + -1v = 0 Solving 9 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1v = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1v = 0 + -9 -1v = 0 + -9 Combine like terms: 0 + -9 = -9 -1v = -9 Divide each side by '-1'. v = 9 Simplifying v = 9Solution
v = {-4, 9}
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