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Simplifying -5 = (p2) + -10p -5 = p2 + -10p Reorder the terms: -5 = -10p + p2 Solving -5 = -10p + p2 Solving for variable 'p'. Reorder the terms: -5 + 10p + -1p2 = -10p + 10p + p2 + -1p2 Combine like terms: -10p + 10p = 0 -5 + 10p + -1p2 = 0 + p2 + -1p2 -5 + 10p + -1p2 = p2 + -1p2 Combine like terms: p2 + -1p2 = 0 -5 + 10p + -1p2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 5 + -10p + p2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + -10p + -5 + p2 = 0 + -5 Reorder the terms: 5 + -5 + -10p + p2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -10p + p2 = 0 + -5 -10p + p2 = 0 + -5 Combine like terms: 0 + -5 = -5 -10p + p2 = -5 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 = -5 + 25 Reorder the terms: 25 + -10p + p2 = -5 + 25 Combine like terms: -5 + 25 = 20 25 + -10p + p2 = 20 Factor a perfect square on the left side: (p + -5)(p + -5) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (p + -5) equal to 4.472135955 and -4.472135955.Subproblem 1
p + -5 = 4.472135955 Simplifying p + -5 = 4.472135955 Reorder the terms: -5 + p = 4.472135955 Solving -5 + p = 4.472135955 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 = 4.472135955 + 5 Combine like terms: -5 + 5 = 0 0 + p = 4.472135955 + 5 p = 4.472135955 + 5 Combine like terms: 4.472135955 + 5 = 9.472135955 p = 9.472135955 Simplifying p = 9.472135955Subproblem 2
p + -5 = -4.472135955 Simplifying p + -5 = -4.472135955 Reorder the terms: -5 + p = -4.472135955 Solving -5 + p = -4.472135955 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 = -4.472135955 + 5 Combine like terms: -5 + 5 = 0 0 + p = -4.472135955 + 5 p = -4.472135955 + 5 Combine like terms: -4.472135955 + 5 = 0.527864045 p = 0.527864045 Simplifying p = 0.527864045Solution
The solution to the problem is based on the solutions from the subproblems. p = {9.472135955, 0.527864045}
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