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Simplifying 3p2 + -60p + 200 = 0 Reorder the terms: 200 + -60p + 3p2 = 0 Solving 200 + -60p + 3p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 66.66666667 + -20p + p2 = 0 Move the constant term to the right: Add '-66.66666667' to each side of the equation. 66.66666667 + -20p + -66.66666667 + p2 = 0 + -66.66666667 Reorder the terms: 66.66666667 + -66.66666667 + -20p + p2 = 0 + -66.66666667 Combine like terms: 66.66666667 + -66.66666667 = 0.00000000 0.00000000 + -20p + p2 = 0 + -66.66666667 -20p + p2 = 0 + -66.66666667 Combine like terms: 0 + -66.66666667 = -66.66666667 -20p + p2 = -66.66666667 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 = -66.66666667 + 100 Reorder the terms: 100 + -20p + p2 = -66.66666667 + 100 Combine like terms: -66.66666667 + 100 = 33.33333333 100 + -20p + p2 = 33.33333333 Factor a perfect square on the left side: (p + -10)(p + -10) = 33.33333333 Calculate the square root of the right side: 5.773502692 Break this problem into two subproblems by setting (p + -10) equal to 5.773502692 and -5.773502692.Subproblem 1
p + -10 = 5.773502692 Simplifying p + -10 = 5.773502692 Reorder the terms: -10 + p = 5.773502692 Solving -10 + p = 5.773502692 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 = 5.773502692 + 10 Combine like terms: -10 + 10 = 0 0 + p = 5.773502692 + 10 p = 5.773502692 + 10 Combine like terms: 5.773502692 + 10 = 15.773502692 p = 15.773502692 Simplifying p = 15.773502692Subproblem 2
p + -10 = -5.773502692 Simplifying p + -10 = -5.773502692 Reorder the terms: -10 + p = -5.773502692 Solving -10 + p = -5.773502692 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 = -5.773502692 + 10 Combine like terms: -10 + 10 = 0 0 + p = -5.773502692 + 10 p = -5.773502692 + 10 Combine like terms: -5.773502692 + 10 = 4.226497308 p = 4.226497308 Simplifying p = 4.226497308Solution
The solution to the problem is based on the solutions from the subproblems. p = {15.773502692, 4.226497308}
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