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Simplifying p2 + 20p = 64 Reorder the terms: 20p + p2 = 64 Solving 20p + p2 = 64 Solving for variable 'p'. Reorder the terms: -64 + 20p + p2 = 64 + -64 Combine like terms: 64 + -64 = 0 -64 + 20p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '64' to each side of the equation. -64 + 20p + 64 + p2 = 0 + 64 Reorder the terms: -64 + 64 + 20p + p2 = 0 + 64 Combine like terms: -64 + 64 = 0 0 + 20p + p2 = 0 + 64 20p + p2 = 0 + 64 Combine like terms: 0 + 64 = 64 20p + p2 = 64 The p term is 20p. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20p + 100 + p2 = 64 + 100 Reorder the terms: 100 + 20p + p2 = 64 + 100 Combine like terms: 64 + 100 = 164 100 + 20p + p2 = 164 Factor a perfect square on the left side: (p + 10)(p + 10) = 164 Calculate the square root of the right side: 12.806248475 Break this problem into two subproblems by setting (p + 10) equal to 12.806248475 and -12.806248475.Subproblem 1
p + 10 = 12.806248475 Simplifying p + 10 = 12.806248475 Reorder the terms: 10 + p = 12.806248475 Solving 10 + p = 12.806248475 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + p = 12.806248475 + -10 Combine like terms: 10 + -10 = 0 0 + p = 12.806248475 + -10 p = 12.806248475 + -10 Combine like terms: 12.806248475 + -10 = 2.806248475 p = 2.806248475 Simplifying p = 2.806248475Subproblem 2
p + 10 = -12.806248475 Simplifying p + 10 = -12.806248475 Reorder the terms: 10 + p = -12.806248475 Solving 10 + p = -12.806248475 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + p = -12.806248475 + -10 Combine like terms: 10 + -10 = 0 0 + p = -12.806248475 + -10 p = -12.806248475 + -10 Combine like terms: -12.806248475 + -10 = -22.806248475 p = -22.806248475 Simplifying p = -22.806248475Solution
The solution to the problem is based on the solutions from the subproblems. p = {2.806248475, -22.806248475}
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