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Simplifying I(p) = p(50 + -1p) Multiply I * p pI = p(50 + -1p) pI = (50 * p + -1p * p) pI = (50p + -1p2) Solving pI = 50p + -1p2 Solving for variable 'p'. Reorder the terms: -50p + pI + p2 = 50p + -1p2 + -50p + p2 Reorder the terms: -50p + pI + p2 = 50p + -50p + -1p2 + p2 Combine like terms: 50p + -50p = 0 -50p + pI + p2 = 0 + -1p2 + p2 -50p + pI + p2 = -1p2 + p2 Combine like terms: -1p2 + p2 = 0 -50p + pI + p2 = 0 Factor out the Greatest Common Factor (GCF), 'p'. p(-50 + I + p) = 0Subproblem 1
Set the factor 'p' equal to zero and attempt to solve: Simplifying p = 0 Solving p = 0 Move all terms containing p to the left, all other terms to the right. Simplifying p = 0Subproblem 2
Set the factor '(-50 + I + p)' equal to zero and attempt to solve: Simplifying -50 + I + p = 0 Solving -50 + I + p = 0 Move all terms containing p to the left, all other terms to the right. Add '50' to each side of the equation. -50 + I + 50 + p = 0 + 50 Reorder the terms: -50 + 50 + I + p = 0 + 50 Combine like terms: -50 + 50 = 0 0 + I + p = 0 + 50 I + p = 0 + 50 Combine like terms: 0 + 50 = 50 I + p = 50 Add '-1I' to each side of the equation. I + -1I + p = 50 + -1I Combine like terms: I + -1I = 0 0 + p = 50 + -1I p = 50 + -1I Simplifying p = 50 + -1ISolution
p = {0, 50 + -1I}
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