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Simplifying 12v2 = 24 + 28v Solving 12v2 = 24 + 28v Solving for variable 'v'. Reorder the terms: -24 + -28v + 12v2 = 24 + 28v + -24 + -28v Reorder the terms: -24 + -28v + 12v2 = 24 + -24 + 28v + -28v Combine like terms: 24 + -24 = 0 -24 + -28v + 12v2 = 0 + 28v + -28v -24 + -28v + 12v2 = 28v + -28v Combine like terms: 28v + -28v = 0 -24 + -28v + 12v2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-6 + -7v + 3v2) = 0 Factor a trinomial. 4((-2 + -3v)(3 + -1v)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-2 + -3v)' equal to zero and attempt to solve: Simplifying -2 + -3v = 0 Solving -2 + -3v = 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 + -3v = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -3v = 0 + 2 -3v = 0 + 2 Combine like terms: 0 + 2 = 2 -3v = 2 Divide each side by '-3'. v = -0.6666666667 Simplifying v = -0.6666666667Subproblem 2
Set the factor '(3 + -1v)' equal to zero and attempt to solve: Simplifying 3 + -1v = 0 Solving 3 + -1v = 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 + -1v = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1v = 0 + -3 -1v = 0 + -3 Combine like terms: 0 + -3 = -3 -1v = -3 Divide each side by '-1'. v = 3 Simplifying v = 3Solution
v = {-0.6666666667, 3}
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