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Simplifying 5v2 = 55v + -140 Reorder the terms: 5v2 = -140 + 55v Solving 5v2 = -140 + 55v Solving for variable 'v'. Reorder the terms: 140 + -55v + 5v2 = -140 + 55v + 140 + -55v Reorder the terms: 140 + -55v + 5v2 = -140 + 140 + 55v + -55v Combine like terms: -140 + 140 = 0 140 + -55v + 5v2 = 0 + 55v + -55v 140 + -55v + 5v2 = 55v + -55v Combine like terms: 55v + -55v = 0 140 + -55v + 5v2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(28 + -11v + v2) = 0 Factor a trinomial. 5((4 + -1v)(7 + -1v)) = 0 Ignore the factor 5.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 '(7 + -1v)' equal to zero and attempt to solve: Simplifying 7 + -1v = 0 Solving 7 + -1v = 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 + -1v = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1v = 0 + -7 -1v = 0 + -7 Combine like terms: 0 + -7 = -7 -1v = -7 Divide each side by '-1'. v = 7 Simplifying v = 7Solution
v = {4, 7}
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