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Simplifying 8v2 = 10 + -16v Solving 8v2 = 10 + -16v Solving for variable 'v'. Reorder the terms: -10 + 16v + 8v2 = 10 + -16v + -10 + 16v Reorder the terms: -10 + 16v + 8v2 = 10 + -10 + -16v + 16v Combine like terms: 10 + -10 = 0 -10 + 16v + 8v2 = 0 + -16v + 16v -10 + 16v + 8v2 = -16v + 16v Combine like terms: -16v + 16v = 0 -10 + 16v + 8v2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + 8v + 4v2) = 0 Factor a trinomial. 2((-5 + -2v)(1 + -2v)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + -2v)' equal to zero and attempt to solve: Simplifying -5 + -2v = 0 Solving -5 + -2v = 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 + -2v = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2v = 0 + 5 -2v = 0 + 5 Combine like terms: 0 + 5 = 5 -2v = 5 Divide each side by '-2'. v = -2.5 Simplifying v = -2.5Subproblem 2
Set the factor '(1 + -2v)' equal to zero and attempt to solve: Simplifying 1 + -2v = 0 Solving 1 + -2v = 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 + -2v = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2v = 0 + -1 -2v = 0 + -1 Combine like terms: 0 + -1 = -1 -2v = -1 Divide each side by '-2'. v = 0.5 Simplifying v = 0.5Solution
v = {-2.5, 0.5}
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