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Simplifying 4v2 + -10v + -75 = 9 Reorder the terms: -75 + -10v + 4v2 = 9 Solving -75 + -10v + 4v2 = 9 Solving for variable 'v'. Reorder the terms: -75 + -9 + -10v + 4v2 = 9 + -9 Combine like terms: -75 + -9 = -84 -84 + -10v + 4v2 = 9 + -9 Combine like terms: 9 + -9 = 0 -84 + -10v + 4v2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-42 + -5v + 2v2) = 0 Factor a trinomial. 2((-7 + -2v)(6 + -1v)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7 + -2v)' equal to zero and attempt to solve: Simplifying -7 + -2v = 0 Solving -7 + -2v = 0 Move all terms containing v to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -2v = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -2v = 0 + 7 -2v = 0 + 7 Combine like terms: 0 + 7 = 7 -2v = 7 Divide each side by '-2'. v = -3.5 Simplifying v = -3.5Subproblem 2
Set the factor '(6 + -1v)' equal to zero and attempt to solve: Simplifying 6 + -1v = 0 Solving 6 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1v = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1v = 0 + -6 -1v = 0 + -6 Combine like terms: 0 + -6 = -6 -1v = -6 Divide each side by '-1'. v = 6 Simplifying v = 6Solution
v = {-3.5, 6}
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