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Simplifying 2v(v + 9) + -1(v + 9) = 0 Reorder the terms: 2v(9 + v) + -1(v + 9) = 0 (9 * 2v + v * 2v) + -1(v + 9) = 0 (18v + 2v2) + -1(v + 9) = 0 Reorder the terms: 18v + 2v2 + -1(9 + v) = 0 18v + 2v2 + (9 * -1 + v * -1) = 0 18v + 2v2 + (-9 + -1v) = 0 Reorder the terms: -9 + 18v + -1v + 2v2 = 0 Combine like terms: 18v + -1v = 17v -9 + 17v + 2v2 = 0 Solving -9 + 17v + 2v2 = 0 Solving for variable 'v'. Factor a trinomial. (-9 + -1v)(1 + -2v) = 0Subproblem 1
Set the factor '(-9 + -1v)' equal to zero and attempt to solve: Simplifying -9 + -1v = 0 Solving -9 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1v = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1v = 0 + 9 -1v = 0 + 9 Combine like terms: 0 + 9 = 9 -1v = 9 Divide each side by '-1'. v = -9 Simplifying v = -9Subproblem 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 = {-9, 0.5}
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