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Simplifying v2 + -2v = 40 + 4v Reorder the terms: -2v + v2 = 40 + 4v Solving -2v + v2 = 40 + 4v Solving for variable 'v'. Reorder the terms: -40 + -2v + -4v + v2 = 40 + 4v + -40 + -4v Combine like terms: -2v + -4v = -6v -40 + -6v + v2 = 40 + 4v + -40 + -4v Reorder the terms: -40 + -6v + v2 = 40 + -40 + 4v + -4v Combine like terms: 40 + -40 = 0 -40 + -6v + v2 = 0 + 4v + -4v -40 + -6v + v2 = 4v + -4v Combine like terms: 4v + -4v = 0 -40 + -6v + v2 = 0 Factor a trinomial. (-4 + -1v)(10 + -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 '(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 = {-4, 10}
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