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