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Simplifying -30v = 9v2 + 25 Reorder the terms: -30v = 25 + 9v2 Solving -30v = 25 + 9v2 Solving for variable 'v'. Reorder the terms: -25 + -30v + -9v2 = 25 + 9v2 + -25 + -9v2 Reorder the terms: -25 + -30v + -9v2 = 25 + -25 + 9v2 + -9v2 Combine like terms: 25 + -25 = 0 -25 + -30v + -9v2 = 0 + 9v2 + -9v2 -25 + -30v + -9v2 = 9v2 + -9v2 Combine like terms: 9v2 + -9v2 = 0 -25 + -30v + -9v2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(25 + 30v + 9v2) = 0 Factor a trinomial. -1((5 + 3v)(5 + 3v)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(5 + 3v)' equal to zero and attempt to solve: Simplifying 5 + 3v = 0 Solving 5 + 3v = 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 + 3v = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3v = 0 + -5 3v = 0 + -5 Combine like terms: 0 + -5 = -5 3v = -5 Divide each side by '3'. v = -1.666666667 Simplifying v = -1.666666667Subproblem 2
Set the factor '(5 + 3v)' equal to zero and attempt to solve: Simplifying 5 + 3v = 0 Solving 5 + 3v = 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 + 3v = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3v = 0 + -5 3v = 0 + -5 Combine like terms: 0 + -5 = -5 3v = -5 Divide each side by '3'. v = -1.666666667 Simplifying v = -1.666666667Solution
v = {-1.666666667, -1.666666667}
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