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Simplifying 4v2 + 8v + -41 = 4 Reorder the terms: -41 + 8v + 4v2 = 4 Solving -41 + 8v + 4v2 = 4 Solving for variable 'v'. Reorder the terms: -41 + -4 + 8v + 4v2 = 4 + -4 Combine like terms: -41 + -4 = -45 -45 + 8v + 4v2 = 4 + -4 Combine like terms: 4 + -4 = 0 -45 + 8v + 4v2 = 0 Factor a trinomial. (-9 + -2v)(5 + -2v) = 0Subproblem 1
Set the factor '(-9 + -2v)' equal to zero and attempt to solve: Simplifying -9 + -2v = 0 Solving -9 + -2v = 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 + -2v = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -2v = 0 + 9 -2v = 0 + 9 Combine like terms: 0 + 9 = 9 -2v = 9 Divide each side by '-2'. v = -4.5 Simplifying v = -4.5Subproblem 2
Set the factor '(5 + -2v)' equal to zero and attempt to solve: Simplifying 5 + -2v = 0 Solving 5 + -2v = 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 + -2v = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2v = 0 + -5 -2v = 0 + -5 Combine like terms: 0 + -5 = -5 -2v = -5 Divide each side by '-2'. v = 2.5 Simplifying v = 2.5Solution
v = {-4.5, 2.5}
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