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Simplifying p2 + -100p + 200 = 0 Reorder the terms: 200 + -100p + p2 = 0 Solving 200 + -100p + p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '-200' to each side of the equation. 200 + -100p + -200 + p2 = 0 + -200 Reorder the terms: 200 + -200 + -100p + p2 = 0 + -200 Combine like terms: 200 + -200 = 0 0 + -100p + p2 = 0 + -200 -100p + p2 = 0 + -200 Combine like terms: 0 + -200 = -200 -100p + p2 = -200 The p term is -100p. Take half its coefficient (-50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. -100p + 2500 + p2 = -200 + 2500 Reorder the terms: 2500 + -100p + p2 = -200 + 2500 Combine like terms: -200 + 2500 = 2300 2500 + -100p + p2 = 2300 Factor a perfect square on the left side: (p + -50)(p + -50) = 2300 Calculate the square root of the right side: 47.958315233 Break this problem into two subproblems by setting (p + -50) equal to 47.958315233 and -47.958315233.Subproblem 1
p + -50 = 47.958315233 Simplifying p + -50 = 47.958315233 Reorder the terms: -50 + p = 47.958315233 Solving -50 + p = 47.958315233 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + p = 47.958315233 + 50 Combine like terms: -50 + 50 = 0 0 + p = 47.958315233 + 50 p = 47.958315233 + 50 Combine like terms: 47.958315233 + 50 = 97.958315233 p = 97.958315233 Simplifying p = 97.958315233Subproblem 2
p + -50 = -47.958315233 Simplifying p + -50 = -47.958315233 Reorder the terms: -50 + p = -47.958315233 Solving -50 + p = -47.958315233 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + p = -47.958315233 + 50 Combine like terms: -50 + 50 = 0 0 + p = -47.958315233 + 50 p = -47.958315233 + 50 Combine like terms: -47.958315233 + 50 = 2.041684767 p = 2.041684767 Simplifying p = 2.041684767Solution
The solution to the problem is based on the solutions from the subproblems. p = {97.958315233, 2.041684767}
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