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Simplifying p2(p2 + -4) = 3p2 + -8 Reorder the terms: p2(-4 + p2) = 3p2 + -8 (-4 * p2 + p2 * p2) = 3p2 + -8 (-4p2 + p4) = 3p2 + -8 Reorder the terms: -4p2 + p4 = -8 + 3p2 Solving -4p2 + p4 = -8 + 3p2 Solving for variable 'p'. Reorder the terms: 8 + -4p2 + -3p2 + p4 = -8 + 3p2 + 8 + -3p2 Combine like terms: -4p2 + -3p2 = -7p2 8 + -7p2 + p4 = -8 + 3p2 + 8 + -3p2 Reorder the terms: 8 + -7p2 + p4 = -8 + 8 + 3p2 + -3p2 Combine like terms: -8 + 8 = 0 8 + -7p2 + p4 = 0 + 3p2 + -3p2 8 + -7p2 + p4 = 3p2 + -3p2 Combine like terms: 3p2 + -3p2 = 0 8 + -7p2 + p4 = 0 Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + -7p2 + -8 + p4 = 0 + -8 Reorder the terms: 8 + -8 + -7p2 + p4 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -7p2 + p4 = 0 + -8 -7p2 + p4 = 0 + -8 Combine like terms: 0 + -8 = -8 -7p2 + p4 = -8 The p term is -7p2. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7p2 + 12.25 + p4 = -8 + 12.25 Reorder the terms: 12.25 + -7p2 + p4 = -8 + 12.25 Combine like terms: -8 + 12.25 = 4.25 12.25 + -7p2 + p4 = 4.25 Factor a perfect square on the left side: (p2 + -3.5)(p2 + -3.5) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (p2 + -3.5) equal to 2.061552813 and -2.061552813.Subproblem 1
p2 + -3.5 = 2.061552813 Simplifying p2 + -3.5 = 2.061552813 Reorder the terms: -3.5 + p2 = 2.061552813 Solving -3.5 + p2 = 2.061552813 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + p2 = 2.061552813 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + p2 = 2.061552813 + 3.5 p2 = 2.061552813 + 3.5 Combine like terms: 2.061552813 + 3.5 = 5.561552813 p2 = 5.561552813 Simplifying p2 = 5.561552813 Take the square root of each side: p = {-2.358294471, 2.358294471}Subproblem 2
p2 + -3.5 = -2.061552813 Simplifying p2 + -3.5 = -2.061552813 Reorder the terms: -3.5 + p2 = -2.061552813 Solving -3.5 + p2 = -2.061552813 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + p2 = -2.061552813 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + p2 = -2.061552813 + 3.5 p2 = -2.061552813 + 3.5 Combine like terms: -2.061552813 + 3.5 = 1.438447187 p2 = 1.438447187 Simplifying p2 = 1.438447187 Take the square root of each side: p = {-1.19935282, 1.19935282}Solution
The solution to the problem is based on the solutions from the subproblems. p = {-2.358294471, 2.358294471, -1.19935282, 1.19935282}
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