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Simplifying p2 + -200p + 2500 = 0 Reorder the terms: 2500 + -200p + p2 = 0 Solving 2500 + -200p + p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '-2500' to each side of the equation. 2500 + -200p + -2500 + p2 = 0 + -2500 Reorder the terms: 2500 + -2500 + -200p + p2 = 0 + -2500 Combine like terms: 2500 + -2500 = 0 0 + -200p + p2 = 0 + -2500 -200p + p2 = 0 + -2500 Combine like terms: 0 + -2500 = -2500 -200p + p2 = -2500 The p term is -200p. Take half its coefficient (-100). Square it (10000) and add it to both sides. Add '10000' to each side of the equation. -200p + 10000 + p2 = -2500 + 10000 Reorder the terms: 10000 + -200p + p2 = -2500 + 10000 Combine like terms: -2500 + 10000 = 7500 10000 + -200p + p2 = 7500 Factor a perfect square on the left side: (p + -100)(p + -100) = 7500 Calculate the square root of the right side: 86.602540378 Break this problem into two subproblems by setting (p + -100) equal to 86.602540378 and -86.602540378.Subproblem 1
p + -100 = 86.602540378 Simplifying p + -100 = 86.602540378 Reorder the terms: -100 + p = 86.602540378 Solving -100 + p = 86.602540378 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + p = 86.602540378 + 100 Combine like terms: -100 + 100 = 0 0 + p = 86.602540378 + 100 p = 86.602540378 + 100 Combine like terms: 86.602540378 + 100 = 186.602540378 p = 186.602540378 Simplifying p = 186.602540378Subproblem 2
p + -100 = -86.602540378 Simplifying p + -100 = -86.602540378 Reorder the terms: -100 + p = -86.602540378 Solving -100 + p = -86.602540378 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + p = -86.602540378 + 100 Combine like terms: -100 + 100 = 0 0 + p = -86.602540378 + 100 p = -86.602540378 + 100 Combine like terms: -86.602540378 + 100 = 13.397459622 p = 13.397459622 Simplifying p = 13.397459622Solution
The solution to the problem is based on the solutions from the subproblems. p = {186.602540378, 13.397459622}
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