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Simplifying -1p2 + 4 = -8p Reorder the terms: 4 + -1p2 = -8p Solving 4 + -1p2 = -8p Solving for variable 'p'. Reorder the terms: 4 + 8p + -1p2 = -8p + 8p Combine like terms: -8p + 8p = 0 4 + 8p + -1p2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -4 + -8p + p2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -8p + 4 + p2 = 0 + 4 Reorder the terms: -4 + 4 + -8p + p2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -8p + p2 = 0 + 4 -8p + p2 = 0 + 4 Combine like terms: 0 + 4 = 4 -8p + p2 = 4 The p term is -8p. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8p + 16 + p2 = 4 + 16 Reorder the terms: 16 + -8p + p2 = 4 + 16 Combine like terms: 4 + 16 = 20 16 + -8p + p2 = 20 Factor a perfect square on the left side: (p + -4)(p + -4) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (p + -4) equal to 4.472135955 and -4.472135955.Subproblem 1
p + -4 = 4.472135955 Simplifying p + -4 = 4.472135955 Reorder the terms: -4 + p = 4.472135955 Solving -4 + p = 4.472135955 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + p = 4.472135955 + 4 Combine like terms: -4 + 4 = 0 0 + p = 4.472135955 + 4 p = 4.472135955 + 4 Combine like terms: 4.472135955 + 4 = 8.472135955 p = 8.472135955 Simplifying p = 8.472135955Subproblem 2
p + -4 = -4.472135955 Simplifying p + -4 = -4.472135955 Reorder the terms: -4 + p = -4.472135955 Solving -4 + p = -4.472135955 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + p = -4.472135955 + 4 Combine like terms: -4 + 4 = 0 0 + p = -4.472135955 + 4 p = -4.472135955 + 4 Combine like terms: -4.472135955 + 4 = -0.472135955 p = -0.472135955 Simplifying p = -0.472135955Solution
The solution to the problem is based on the solutions from the subproblems. p = {8.472135955, -0.472135955}
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