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Simplifying 8v2 + 16v + -57 = 7 Reorder the terms: -57 + 16v + 8v2 = 7 Solving -57 + 16v + 8v2 = 7 Solving for variable 'v'. Reorder the terms: -57 + -7 + 16v + 8v2 = 7 + -7 Combine like terms: -57 + -7 = -64 -64 + 16v + 8v2 = 7 + -7 Combine like terms: 7 + -7 = 0 -64 + 16v + 8v2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-8 + 2v + v2) = 0 Factor a trinomial. 8((-4 + -1v)(2 + -1v)) = 0 Ignore the factor 8.Subproblem 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 '(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 = {-4, 2}
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