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Simplifying (9v + -5)(v + 5) = 0 Reorder the terms: (-5 + 9v)(v + 5) = 0 Reorder the terms: (-5 + 9v)(5 + v) = 0 Multiply (-5 + 9v) * (5 + v) (-5(5 + v) + 9v * (5 + v)) = 0 ((5 * -5 + v * -5) + 9v * (5 + v)) = 0 ((-25 + -5v) + 9v * (5 + v)) = 0 (-25 + -5v + (5 * 9v + v * 9v)) = 0 (-25 + -5v + (45v + 9v2)) = 0 Combine like terms: -5v + 45v = 40v (-25 + 40v + 9v2) = 0 Solving -25 + 40v + 9v2 = 0 Solving for variable 'v'. Factor a trinomial. (-5 + -1v)(5 + -9v) = 0Subproblem 1
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 = -5Subproblem 2
Set the factor '(5 + -9v)' equal to zero and attempt to solve: Simplifying 5 + -9v = 0 Solving 5 + -9v = 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 + -9v = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -9v = 0 + -5 -9v = 0 + -5 Combine like terms: 0 + -5 = -5 -9v = -5 Divide each side by '-9'. v = 0.5555555556 Simplifying v = 0.5555555556Solution
v = {-5, 0.5555555556}
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