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Simplifying v2 + -1v = 21 + 3v Reorder the terms: -1v + v2 = 21 + 3v Solving -1v + v2 = 21 + 3v Solving for variable 'v'. Reorder the terms: -21 + -1v + -3v + v2 = 21 + 3v + -21 + -3v Combine like terms: -1v + -3v = -4v -21 + -4v + v2 = 21 + 3v + -21 + -3v Reorder the terms: -21 + -4v + v2 = 21 + -21 + 3v + -3v Combine like terms: 21 + -21 = 0 -21 + -4v + v2 = 0 + 3v + -3v -21 + -4v + v2 = 3v + -3v Combine like terms: 3v + -3v = 0 -21 + -4v + v2 = 0 Factor a trinomial. (-3 + -1v)(7 + -1v) = 0Subproblem 1
Set the factor '(-3 + -1v)' equal to zero and attempt to solve: Simplifying -3 + -1v = 0 Solving -3 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1v = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1v = 0 + 3 -1v = 0 + 3 Combine like terms: 0 + 3 = 3 -1v = 3 Divide each side by '-1'. v = -3 Simplifying v = -3Subproblem 2
Set the factor '(7 + -1v)' equal to zero and attempt to solve: Simplifying 7 + -1v = 0 Solving 7 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1v = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1v = 0 + -7 -1v = 0 + -7 Combine like terms: 0 + -7 = -7 -1v = -7 Divide each side by '-1'. v = 7 Simplifying v = 7Solution
v = {-3, 7}
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