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Simplifying p2 + -10p + -84 = -10 Reorder the terms: -84 + -10p + p2 = -10 Solving -84 + -10p + p2 = -10 Solving for variable 'p'. Reorder the terms: -84 + 10 + -10p + p2 = -10 + 10 Combine like terms: -84 + 10 = -74 -74 + -10p + p2 = -10 + 10 Combine like terms: -10 + 10 = 0 -74 + -10p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '74' to each side of the equation. -74 + -10p + 74 + p2 = 0 + 74 Reorder the terms: -74 + 74 + -10p + p2 = 0 + 74 Combine like terms: -74 + 74 = 0 0 + -10p + p2 = 0 + 74 -10p + p2 = 0 + 74 Combine like terms: 0 + 74 = 74 -10p + p2 = 74 The p term is -10p. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10p + 25 + p2 = 74 + 25 Reorder the terms: 25 + -10p + p2 = 74 + 25 Combine like terms: 74 + 25 = 99 25 + -10p + p2 = 99 Factor a perfect square on the left side: (p + -5)(p + -5) = 99 Calculate the square root of the right side: 9.949874371 Break this problem into two subproblems by setting (p + -5) equal to 9.949874371 and -9.949874371.Subproblem 1
p + -5 = 9.949874371 Simplifying p + -5 = 9.949874371 Reorder the terms: -5 + p = 9.949874371 Solving -5 + p = 9.949874371 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + p = 9.949874371 + 5 Combine like terms: -5 + 5 = 0 0 + p = 9.949874371 + 5 p = 9.949874371 + 5 Combine like terms: 9.949874371 + 5 = 14.949874371 p = 14.949874371 Simplifying p = 14.949874371Subproblem 2
p + -5 = -9.949874371 Simplifying p + -5 = -9.949874371 Reorder the terms: -5 + p = -9.949874371 Solving -5 + p = -9.949874371 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + p = -9.949874371 + 5 Combine like terms: -5 + 5 = 0 0 + p = -9.949874371 + 5 p = -9.949874371 + 5 Combine like terms: -9.949874371 + 5 = -4.949874371 p = -4.949874371 Simplifying p = -4.949874371Solution
The solution to the problem is based on the solutions from the subproblems. p = {14.949874371, -4.949874371}
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