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Simplifying p4 + -8p2 + 3 = 0 Reorder the terms: 3 + -8p2 + p4 = 0 Solving 3 + -8p2 + p4 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -8p2 + -3 + p4 = 0 + -3 Reorder the terms: 3 + -3 + -8p2 + p4 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -8p2 + p4 = 0 + -3 -8p2 + p4 = 0 + -3 Combine like terms: 0 + -3 = -3 -8p2 + p4 = -3 The p term is -8p2. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8p2 + 16 + p4 = -3 + 16 Reorder the terms: 16 + -8p2 + p4 = -3 + 16 Combine like terms: -3 + 16 = 13 16 + -8p2 + p4 = 13 Factor a perfect square on the left side: (p2 + -4)(p2 + -4) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (p2 + -4) equal to 3.605551275 and -3.605551275.Subproblem 1
p2 + -4 = 3.605551275 Simplifying p2 + -4 = 3.605551275 Reorder the terms: -4 + p2 = 3.605551275 Solving -4 + p2 = 3.605551275 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 + p2 = 3.605551275 + 4 Combine like terms: -4 + 4 = 0 0 + p2 = 3.605551275 + 4 p2 = 3.605551275 + 4 Combine like terms: 3.605551275 + 4 = 7.605551275 p2 = 7.605551275 Simplifying p2 = 7.605551275 Take the square root of each side: p = {-2.757816396, 2.757816396}Subproblem 2
p2 + -4 = -3.605551275 Simplifying p2 + -4 = -3.605551275 Reorder the terms: -4 + p2 = -3.605551275 Solving -4 + p2 = -3.605551275 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 + p2 = -3.605551275 + 4 Combine like terms: -4 + 4 = 0 0 + p2 = -3.605551275 + 4 p2 = -3.605551275 + 4 Combine like terms: -3.605551275 + 4 = 0.394448725 p2 = 0.394448725 Simplifying p2 = 0.394448725 Take the square root of each side: p = {-0.628051531, 0.628051531}Solution
The solution to the problem is based on the solutions from the subproblems. p = {-2.757816396, 2.757816396, -0.628051531, 0.628051531}
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