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Simplifying v * v + 2v + 5 = 8 Multiply v * v v2 + 2v + 5 = 8 Reorder the terms: 5 + 2v + v2 = 8 Solving 5 + 2v + v2 = 8 Solving for variable 'v'. Reorder the terms: 5 + -8 + 2v + v2 = 8 + -8 Combine like terms: 5 + -8 = -3 -3 + 2v + v2 = 8 + -8 Combine like terms: 8 + -8 = 0 -3 + 2v + v2 = 0 Factor a trinomial. (-3 + -1v)(1 + -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 '(1 + -1v)' equal to zero and attempt to solve: Simplifying 1 + -1v = 0 Solving 1 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1v = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1v = 0 + -1 -1v = 0 + -1 Combine like terms: 0 + -1 = -1 -1v = -1 Divide each side by '-1'. v = 1 Simplifying v = 1Solution
v = {-3, 1}
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