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Simplifying 14v2 + 46v + -47 = -7 Reorder the terms: -47 + 46v + 14v2 = -7 Solving -47 + 46v + 14v2 = -7 Solving for variable 'v'. Reorder the terms: -47 + 7 + 46v + 14v2 = -7 + 7 Combine like terms: -47 + 7 = -40 -40 + 46v + 14v2 = -7 + 7 Combine like terms: -7 + 7 = 0 -40 + 46v + 14v2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-20 + 23v + 7v2) = 0 Factor a trinomial. 2((-4 + -1v)(5 + -7v)) = 0 Ignore the factor 2.Subproblem 1
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 = -4Subproblem 2
Set the factor '(5 + -7v)' equal to zero and attempt to solve: Simplifying 5 + -7v = 0 Solving 5 + -7v = 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 + -7v = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -7v = 0 + -5 -7v = 0 + -5 Combine like terms: 0 + -5 = -5 -7v = -5 Divide each side by '-7'. v = 0.7142857143 Simplifying v = 0.7142857143Solution
v = {-4, 0.7142857143}
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