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Simplifying 25600p = (p + 12)(-1p + 20) Reorder the terms: 25600p = (12 + p)(-1p + 20) Reorder the terms: 25600p = (12 + p)(20 + -1p) Multiply (12 + p) * (20 + -1p) 25600p = (12(20 + -1p) + p(20 + -1p)) 25600p = ((20 * 12 + -1p * 12) + p(20 + -1p)) 25600p = ((240 + -12p) + p(20 + -1p)) 25600p = (240 + -12p + (20 * p + -1p * p)) 25600p = (240 + -12p + (20p + -1p2)) Combine like terms: -12p + 20p = 8p 25600p = (240 + 8p + -1p2) Solving 25600p = 240 + 8p + -1p2 Solving for variable 'p'. Reorder the terms: -240 + 25600p + -8p + p2 = 240 + 8p + -1p2 + -240 + -8p + p2 Combine like terms: 25600p + -8p = 25592p -240 + 25592p + p2 = 240 + 8p + -1p2 + -240 + -8p + p2 Reorder the terms: -240 + 25592p + p2 = 240 + -240 + 8p + -8p + -1p2 + p2 Combine like terms: 240 + -240 = 0 -240 + 25592p + p2 = 0 + 8p + -8p + -1p2 + p2 -240 + 25592p + p2 = 8p + -8p + -1p2 + p2 Combine like terms: 8p + -8p = 0 -240 + 25592p + p2 = 0 + -1p2 + p2 -240 + 25592p + p2 = -1p2 + p2 Combine like terms: -1p2 + p2 = 0 -240 + 25592p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '240' to each side of the equation. -240 + 25592p + 240 + p2 = 0 + 240 Reorder the terms: -240 + 240 + 25592p + p2 = 0 + 240 Combine like terms: -240 + 240 = 0 0 + 25592p + p2 = 0 + 240 25592p + p2 = 0 + 240 Combine like terms: 0 + 240 = 240 25592p + p2 = 240 The p term is 25592p. Take half its coefficient (12796). Square it (163737616) and add it to both sides. Add '163737616' to each side of the equation. 25592p + 163737616 + p2 = 240 + 163737616 Reorder the terms: 163737616 + 25592p + p2 = 240 + 163737616 Combine like terms: 240 + 163737616 = 163737856 163737616 + 25592p + p2 = 163737856 Factor a perfect square on the left side: (p + 12796)(p + 12796) = 163737856 Calculate the square root of the right side: 12796.009377927 Break this problem into two subproblems by setting (p + 12796) equal to 12796.009377927 and -12796.009377927.Subproblem 1
p + 12796 = 12796.009377927 Simplifying p + 12796 = 12796.009377927 Reorder the terms: 12796 + p = 12796.009377927 Solving 12796 + p = 12796.009377927 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-12796' to each side of the equation. 12796 + -12796 + p = 12796.009377927 + -12796 Combine like terms: 12796 + -12796 = 0 0 + p = 12796.009377927 + -12796 p = 12796.009377927 + -12796 Combine like terms: 12796.009377927 + -12796 = 0.009377927 p = 0.009377927 Simplifying p = 0.009377927Subproblem 2
p + 12796 = -12796.009377927 Simplifying p + 12796 = -12796.009377927 Reorder the terms: 12796 + p = -12796.009377927 Solving 12796 + p = -12796.009377927 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-12796' to each side of the equation. 12796 + -12796 + p = -12796.009377927 + -12796 Combine like terms: 12796 + -12796 = 0 0 + p = -12796.009377927 + -12796 p = -12796.009377927 + -12796 Combine like terms: -12796.009377927 + -12796 = -25592.009377927 p = -25592.009377927 Simplifying p = -25592.009377927Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.009377927, -25592.009377927}
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