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Simplifying p2 + -250p = 50 Reorder the terms: -250p + p2 = 50 Solving -250p + p2 = 50 Solving for variable 'p'. Reorder the terms: -50 + -250p + p2 = 50 + -50 Combine like terms: 50 + -50 = 0 -50 + -250p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '50' to each side of the equation. -50 + -250p + 50 + p2 = 0 + 50 Reorder the terms: -50 + 50 + -250p + p2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + -250p + p2 = 0 + 50 -250p + p2 = 0 + 50 Combine like terms: 0 + 50 = 50 -250p + p2 = 50 The p term is -250p. Take half its coefficient (-125). Square it (15625) and add it to both sides. Add '15625' to each side of the equation. -250p + 15625 + p2 = 50 + 15625 Reorder the terms: 15625 + -250p + p2 = 50 + 15625 Combine like terms: 50 + 15625 = 15675 15625 + -250p + p2 = 15675 Factor a perfect square on the left side: (p + -125)(p + -125) = 15675 Calculate the square root of the right side: 125.199840255 Break this problem into two subproblems by setting (p + -125) equal to 125.199840255 and -125.199840255.Subproblem 1
p + -125 = 125.199840255 Simplifying p + -125 = 125.199840255 Reorder the terms: -125 + p = 125.199840255 Solving -125 + p = 125.199840255 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '125' to each side of the equation. -125 + 125 + p = 125.199840255 + 125 Combine like terms: -125 + 125 = 0 0 + p = 125.199840255 + 125 p = 125.199840255 + 125 Combine like terms: 125.199840255 + 125 = 250.199840255 p = 250.199840255 Simplifying p = 250.199840255Subproblem 2
p + -125 = -125.199840255 Simplifying p + -125 = -125.199840255 Reorder the terms: -125 + p = -125.199840255 Solving -125 + p = -125.199840255 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '125' to each side of the equation. -125 + 125 + p = -125.199840255 + 125 Combine like terms: -125 + 125 = 0 0 + p = -125.199840255 + 125 p = -125.199840255 + 125 Combine like terms: -125.199840255 + 125 = -0.199840255 p = -0.199840255 Simplifying p = -0.199840255Solution
The solution to the problem is based on the solutions from the subproblems. p = {250.199840255, -0.199840255}
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