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Simplifying -3(p + 2) * p + -5 = -4p(p + 4) + 5 Reorder the terms: -3(2 + p) * p + -5 = -4p(p + 4) + 5 Reorder the terms for easier multiplication: -3p(2 + p) + -5 = -4p(p + 4) + 5 (2 * -3p + p * -3p) + -5 = -4p(p + 4) + 5 (-6p + -3p2) + -5 = -4p(p + 4) + 5 Reorder the terms: -5 + -6p + -3p2 = -4p(p + 4) + 5 Reorder the terms: -5 + -6p + -3p2 = -4p(4 + p) + 5 -5 + -6p + -3p2 = (4 * -4p + p * -4p) + 5 -5 + -6p + -3p2 = (-16p + -4p2) + 5 Reorder the terms: -5 + -6p + -3p2 = 5 + -16p + -4p2 Solving -5 + -6p + -3p2 = 5 + -16p + -4p2 Solving for variable 'p'. Reorder the terms: -5 + -5 + -6p + 16p + -3p2 + 4p2 = 5 + -16p + -4p2 + -5 + 16p + 4p2 Combine like terms: -5 + -5 = -10 -10 + -6p + 16p + -3p2 + 4p2 = 5 + -16p + -4p2 + -5 + 16p + 4p2 Combine like terms: -6p + 16p = 10p -10 + 10p + -3p2 + 4p2 = 5 + -16p + -4p2 + -5 + 16p + 4p2 Combine like terms: -3p2 + 4p2 = 1p2 -10 + 10p + 1p2 = 5 + -16p + -4p2 + -5 + 16p + 4p2 Reorder the terms: -10 + 10p + 1p2 = 5 + -5 + -16p + 16p + -4p2 + 4p2 Combine like terms: 5 + -5 = 0 -10 + 10p + 1p2 = 0 + -16p + 16p + -4p2 + 4p2 -10 + 10p + 1p2 = -16p + 16p + -4p2 + 4p2 Combine like terms: -16p + 16p = 0 -10 + 10p + 1p2 = 0 + -4p2 + 4p2 -10 + 10p + 1p2 = -4p2 + 4p2 Combine like terms: -4p2 + 4p2 = 0 -10 + 10p + 1p2 = 0 Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + 10p + 10 + p2 = 0 + 10 Reorder the terms: -10 + 10 + 10p + p2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 10p + p2 = 0 + 10 10p + p2 = 0 + 10 Combine like terms: 0 + 10 = 10 10p + p2 = 10 The p term is 10p. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10p + 25 + p2 = 10 + 25 Reorder the terms: 25 + 10p + p2 = 10 + 25 Combine like terms: 10 + 25 = 35 25 + 10p + p2 = 35 Factor a perfect square on the left side: (p + 5)(p + 5) = 35 Calculate the square root of the right side: 5.916079783 Break this problem into two subproblems by setting (p + 5) equal to 5.916079783 and -5.916079783.Subproblem 1
p + 5 = 5.916079783 Simplifying p + 5 = 5.916079783 Reorder the terms: 5 + p = 5.916079783 Solving 5 + p = 5.916079783 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + p = 5.916079783 + -5 Combine like terms: 5 + -5 = 0 0 + p = 5.916079783 + -5 p = 5.916079783 + -5 Combine like terms: 5.916079783 + -5 = 0.916079783 p = 0.916079783 Simplifying p = 0.916079783Subproblem 2
p + 5 = -5.916079783 Simplifying p + 5 = -5.916079783 Reorder the terms: 5 + p = -5.916079783 Solving 5 + p = -5.916079783 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + p = -5.916079783 + -5 Combine like terms: 5 + -5 = 0 0 + p = -5.916079783 + -5 p = -5.916079783 + -5 Combine like terms: -5.916079783 + -5 = -10.916079783 p = -10.916079783 Simplifying p = -10.916079783Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.916079783, -10.916079783}
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