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Simplifying (2 + -1v)(4v + -9) = 0 Reorder the terms: (2 + -1v)(-9 + 4v) = 0 Multiply (2 + -1v) * (-9 + 4v) (2(-9 + 4v) + -1v * (-9 + 4v)) = 0 ((-9 * 2 + 4v * 2) + -1v * (-9 + 4v)) = 0 ((-18 + 8v) + -1v * (-9 + 4v)) = 0 (-18 + 8v + (-9 * -1v + 4v * -1v)) = 0 (-18 + 8v + (9v + -4v2)) = 0 Combine like terms: 8v + 9v = 17v (-18 + 17v + -4v2) = 0 Solving -18 + 17v + -4v2 = 0 Solving for variable 'v'. Factor a trinomial. (-9 + 4v)(2 + -1v) = 0Subproblem 1
Set the factor '(-9 + 4v)' equal to zero and attempt to solve: Simplifying -9 + 4v = 0 Solving -9 + 4v = 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 + 4v = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 4v = 0 + 9 4v = 0 + 9 Combine like terms: 0 + 9 = 9 4v = 9 Divide each side by '4'. v = 2.25 Simplifying v = 2.25Subproblem 2
Set the factor '(2 + -1v)' equal to zero and attempt to solve: Simplifying 2 + -1v = 0 Solving 2 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1v = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1v = 0 + -2 -1v = 0 + -2 Combine like terms: 0 + -2 = -2 -1v = -2 Divide each side by '-1'. v = 2 Simplifying v = 2Solution
v = {2.25, 2}
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