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Simplifying 3(p + -5) + p(p + 8) = 0 Reorder the terms: 3(-5 + p) + p(p + 8) = 0 (-5 * 3 + p * 3) + p(p + 8) = 0 (-15 + 3p) + p(p + 8) = 0 Reorder the terms: -15 + 3p + p(8 + p) = 0 -15 + 3p + (8 * p + p * p) = 0 -15 + 3p + (8p + p2) = 0 Combine like terms: 3p + 8p = 11p -15 + 11p + p2 = 0 Solving -15 + 11p + p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + 11p + 15 + p2 = 0 + 15 Reorder the terms: -15 + 15 + 11p + p2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 11p + p2 = 0 + 15 11p + p2 = 0 + 15 Combine like terms: 0 + 15 = 15 11p + p2 = 15 The p term is 11p. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11p + 30.25 + p2 = 15 + 30.25 Reorder the terms: 30.25 + 11p + p2 = 15 + 30.25 Combine like terms: 15 + 30.25 = 45.25 30.25 + 11p + p2 = 45.25 Factor a perfect square on the left side: (p + 5.5)(p + 5.5) = 45.25 Calculate the square root of the right side: 6.726812024 Break this problem into two subproblems by setting (p + 5.5) equal to 6.726812024 and -6.726812024.Subproblem 1
p + 5.5 = 6.726812024 Simplifying p + 5.5 = 6.726812024 Reorder the terms: 5.5 + p = 6.726812024 Solving 5.5 + p = 6.726812024 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + p = 6.726812024 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + p = 6.726812024 + -5.5 p = 6.726812024 + -5.5 Combine like terms: 6.726812024 + -5.5 = 1.226812024 p = 1.226812024 Simplifying p = 1.226812024Subproblem 2
p + 5.5 = -6.726812024 Simplifying p + 5.5 = -6.726812024 Reorder the terms: 5.5 + p = -6.726812024 Solving 5.5 + p = -6.726812024 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + p = -6.726812024 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + p = -6.726812024 + -5.5 p = -6.726812024 + -5.5 Combine like terms: -6.726812024 + -5.5 = -12.226812024 p = -12.226812024 Simplifying p = -12.226812024Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.226812024, -12.226812024}
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