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Simplifying v2 + 4vp + -32p2 = 0 Reorder the terms: 4pv + -32p2 + v2 = 0 Solving 4pv + -32p2 + v2 = 0 Solving for variable 'p'. Factor a trinomial. (-8p + -1v)(4p + -1v) = 0Subproblem 1
Set the factor '(-8p + -1v)' equal to zero and attempt to solve: Simplifying -8p + -1v = 0 Solving -8p + -1v = 0 Move all terms containing p to the left, all other terms to the right. Add 'v' to each side of the equation. -8p + -1v + v = 0 + v Combine like terms: -1v + v = 0 -8p + 0 = 0 + v -8p = 0 + v Remove the zero: -8p = v Divide each side by '-8'. p = -0.125v Simplifying p = -0.125vSubproblem 2
Set the factor '(4p + -1v)' equal to zero and attempt to solve: Simplifying 4p + -1v = 0 Solving 4p + -1v = 0 Move all terms containing p to the left, all other terms to the right. Add 'v' to each side of the equation. 4p + -1v + v = 0 + v Combine like terms: -1v + v = 0 4p + 0 = 0 + v 4p = 0 + v Remove the zero: 4p = v Divide each side by '4'. p = 0.25v Simplifying p = 0.25vSolution
p = {-0.125v, 0.25v}
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