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Simplifying 0 = v2 + -7v + 10 Reorder the terms: 0 = 10 + -7v + v2 Solving 0 = 10 + -7v + v2 Solving for variable 'v'. Combine like terms: 0 + -10 = -10 -10 + 7v + -1v2 = 10 + -7v + v2 + -10 + 7v + -1v2 Reorder the terms: -10 + 7v + -1v2 = 10 + -10 + -7v + 7v + v2 + -1v2 Combine like terms: 10 + -10 = 0 -10 + 7v + -1v2 = 0 + -7v + 7v + v2 + -1v2 -10 + 7v + -1v2 = -7v + 7v + v2 + -1v2 Combine like terms: -7v + 7v = 0 -10 + 7v + -1v2 = 0 + v2 + -1v2 -10 + 7v + -1v2 = v2 + -1v2 Combine like terms: v2 + -1v2 = 0 -10 + 7v + -1v2 = 0 Factor a trinomial. (-5 + v)(2 + -1v) = 0Subproblem 1
Set the factor '(-5 + v)' equal to zero and attempt to solve: Simplifying -5 + v = 0 Solving -5 + v = 0 Move all terms containing v to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + v = 0 + 5 Combine like terms: -5 + 5 = 0 0 + v = 0 + 5 v = 0 + 5 Combine like terms: 0 + 5 = 5 v = 5 Simplifying v = 5Subproblem 2
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 = 2Solution
v = {5, 2}
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