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Simplifying 10 = 52v + -10v2 Solving 10 = 52v + -10v2 Solving for variable 'v'. Reorder the terms: 10 + -52v + 10v2 = 52v + -52v + -10v2 + 10v2 Combine like terms: 52v + -52v = 0 10 + -52v + 10v2 = 0 + -10v2 + 10v2 10 + -52v + 10v2 = -10v2 + 10v2 Combine like terms: -10v2 + 10v2 = 0 10 + -52v + 10v2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(5 + -26v + 5v2) = 0 Factor a trinomial. 2((1 + -5v)(5 + -1v)) = 0 Ignore the factor 2.Subproblem 1
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 = 0.2Subproblem 2
Set the factor '(5 + -1v)' equal to zero and attempt to solve: Simplifying 5 + -1v = 0 Solving 5 + -1v = 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 + -1v = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1v = 0 + -5 -1v = 0 + -5 Combine like terms: 0 + -5 = -5 -1v = -5 Divide each side by '-1'. v = 5 Simplifying v = 5Solution
v = {0.2, 5}
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