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Simplifying 10v2 + 38v = 8 Reorder the terms: 38v + 10v2 = 8 Solving 38v + 10v2 = 8 Solving for variable 'v'. Reorder the terms: -8 + 38v + 10v2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + 38v + 10v2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + 19v + 5v2) = 0 Factor a trinomial. 2((-4 + -1v)(1 + -5v)) = 0 Ignore the factor 2.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 '(1 + -5v)' equal to zero and attempt to solve: Simplifying 1 + -5v = 0 Solving 1 + -5v = 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 + -5v = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5v = 0 + -1 -5v = 0 + -1 Combine like terms: 0 + -1 = -1 -5v = -1 Divide each side by '-5'. v = 0.2 Simplifying v = 0.2Solution
v = {-4, 0.2}
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