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Simplifying 4v2 = -28 + 32v Solving 4v2 = -28 + 32v Solving for variable 'v'. Reorder the terms: 28 + -32v + 4v2 = -28 + 32v + 28 + -32v Reorder the terms: 28 + -32v + 4v2 = -28 + 28 + 32v + -32v Combine like terms: -28 + 28 = 0 28 + -32v + 4v2 = 0 + 32v + -32v 28 + -32v + 4v2 = 32v + -32v Combine like terms: 32v + -32v = 0 28 + -32v + 4v2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(7 + -8v + v2) = 0 Factor a trinomial. 4((1 + -1v)(7 + -1v)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(1 + -1v)' equal to zero and attempt to solve: Simplifying 1 + -1v = 0 Solving 1 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1v = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1v = 0 + -1 -1v = 0 + -1 Combine like terms: 0 + -1 = -1 -1v = -1 Divide each side by '-1'. v = 1 Simplifying v = 1Subproblem 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 = {1, 7}
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