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Simplifying 400p4 + -360p2 + 1 = 0 Reorder the terms: 1 + -360p2 + 400p4 = 0 Solving 1 + -360p2 + 400p4 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 400 the coefficient of the squared term: Divide each side by '400'. 0.0025 + -0.9p2 + p4 = 0 Move the constant term to the right: Add '-0.0025' to each side of the equation. 0.0025 + -0.9p2 + -0.0025 + p4 = 0 + -0.0025 Reorder the terms: 0.0025 + -0.0025 + -0.9p2 + p4 = 0 + -0.0025 Combine like terms: 0.0025 + -0.0025 = 0.0000 0.0000 + -0.9p2 + p4 = 0 + -0.0025 -0.9p2 + p4 = 0 + -0.0025 Combine like terms: 0 + -0.0025 = -0.0025 -0.9p2 + p4 = -0.0025 The p term is -0.9p2. Take half its coefficient (-0.45). Square it (0.2025) and add it to both sides. Add '0.2025' to each side of the equation. -0.9p2 + 0.2025 + p4 = -0.0025 + 0.2025 Reorder the terms: 0.2025 + -0.9p2 + p4 = -0.0025 + 0.2025 Combine like terms: -0.0025 + 0.2025 = 0.2 0.2025 + -0.9p2 + p4 = 0.2 Factor a perfect square on the left side: (p2 + -0.45)(p2 + -0.45) = 0.2 Calculate the square root of the right side: 0.447213596 Break this problem into two subproblems by setting (p2 + -0.45) equal to 0.447213596 and -0.447213596.Subproblem 1
p2 + -0.45 = 0.447213596 Simplifying p2 + -0.45 = 0.447213596 Reorder the terms: -0.45 + p2 = 0.447213596 Solving -0.45 + p2 = 0.447213596 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.45' to each side of the equation. -0.45 + 0.45 + p2 = 0.447213596 + 0.45 Combine like terms: -0.45 + 0.45 = 0.00 0.00 + p2 = 0.447213596 + 0.45 p2 = 0.447213596 + 0.45 Combine like terms: 0.447213596 + 0.45 = 0.897213596 p2 = 0.897213596 Simplifying p2 = 0.897213596 Take the square root of each side: p = {-0.947213596, 0.947213596}Subproblem 2
p2 + -0.45 = -0.447213596 Simplifying p2 + -0.45 = -0.447213596 Reorder the terms: -0.45 + p2 = -0.447213596 Solving -0.45 + p2 = -0.447213596 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.45' to each side of the equation. -0.45 + 0.45 + p2 = -0.447213596 + 0.45 Combine like terms: -0.45 + 0.45 = 0.00 0.00 + p2 = -0.447213596 + 0.45 p2 = -0.447213596 + 0.45 Combine like terms: -0.447213596 + 0.45 = 0.002786404 p2 = 0.002786404 Simplifying p2 = 0.002786404 Take the square root of each side: p = {-0.0527864, 0.0527864}Solution
The solution to the problem is based on the solutions from the subproblems. p = {-0.947213596, 0.947213596, -0.0527864, 0.0527864}
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