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Simplifying v2 + -6v = 20 + 2v Reorder the terms: -6v + v2 = 20 + 2v Solving -6v + v2 = 20 + 2v Solving for variable 'v'. Reorder the terms: -20 + -6v + -2v + v2 = 20 + 2v + -20 + -2v Combine like terms: -6v + -2v = -8v -20 + -8v + v2 = 20 + 2v + -20 + -2v Reorder the terms: -20 + -8v + v2 = 20 + -20 + 2v + -2v Combine like terms: 20 + -20 = 0 -20 + -8v + v2 = 0 + 2v + -2v -20 + -8v + v2 = 2v + -2v Combine like terms: 2v + -2v = 0 -20 + -8v + v2 = 0 Factor a trinomial. (-2 + -1v)(10 + -1v) = 0Subproblem 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 = -2Subproblem 2
Set the factor '(10 + -1v)' equal to zero and attempt to solve: Simplifying 10 + -1v = 0 Solving 10 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1v = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1v = 0 + -10 -1v = 0 + -10 Combine like terms: 0 + -10 = -10 -1v = -10 Divide each side by '-1'. v = 10 Simplifying v = 10Solution
v = {-2, 10}
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