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Simplifying 4v2 + -10v + -17 = 7 Reorder the terms: -17 + -10v + 4v2 = 7 Solving -17 + -10v + 4v2 = 7 Solving for variable 'v'. Reorder the terms: -17 + -7 + -10v + 4v2 = 7 + -7 Combine like terms: -17 + -7 = -24 -24 + -10v + 4v2 = 7 + -7 Combine like terms: 7 + -7 = 0 -24 + -10v + 4v2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-12 + -5v + 2v2) = 0 Factor a trinomial. 2((-3 + -2v)(4 + -1v)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -2v)' equal to zero and attempt to solve: Simplifying -3 + -2v = 0 Solving -3 + -2v = 0 Move all terms containing v to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -2v = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2v = 0 + 3 -2v = 0 + 3 Combine like terms: 0 + 3 = 3 -2v = 3 Divide each side by '-2'. v = -1.5 Simplifying v = -1.5Subproblem 2
Set the factor '(4 + -1v)' equal to zero and attempt to solve: Simplifying 4 + -1v = 0 Solving 4 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1v = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1v = 0 + -4 -1v = 0 + -4 Combine like terms: 0 + -4 = -4 -1v = -4 Divide each side by '-1'. v = 4 Simplifying v = 4Solution
v = {-1.5, 4}
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