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Simplifying 2p2 + 4p = 4 Reorder the terms: 4p + 2p2 = 4 Solving 4p + 2p2 = 4 Solving for variable 'p'. Reorder the terms: -4 + 4p + 2p2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + 4p + 2p2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + 2p + p2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + 2p + p2)' equal to zero and attempt to solve: Simplifying -2 + 2p + p2 = 0 Solving -2 + 2p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + 2p + 2 + p2 = 0 + 2 Reorder the terms: -2 + 2 + 2p + p2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 2p + p2 = 0 + 2 2p + p2 = 0 + 2 Combine like terms: 0 + 2 = 2 2p + p2 = 2 The p term is 2p. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2p + 1 + p2 = 2 + 1 Reorder the terms: 1 + 2p + p2 = 2 + 1 Combine like terms: 2 + 1 = 3 1 + 2p + p2 = 3 Factor a perfect square on the left side: (p + 1)(p + 1) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (p + 1) equal to 1.732050808 and -1.732050808.Subproblem 1
p + 1 = 1.732050808 Simplifying p + 1 = 1.732050808 Reorder the terms: 1 + p = 1.732050808 Solving 1 + p = 1.732050808 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + p = 1.732050808 + -1 Combine like terms: 1 + -1 = 0 0 + p = 1.732050808 + -1 p = 1.732050808 + -1 Combine like terms: 1.732050808 + -1 = 0.732050808 p = 0.732050808 Simplifying p = 0.732050808Subproblem 2
p + 1 = -1.732050808 Simplifying p + 1 = -1.732050808 Reorder the terms: 1 + p = -1.732050808 Solving 1 + p = -1.732050808 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + p = -1.732050808 + -1 Combine like terms: 1 + -1 = 0 0 + p = -1.732050808 + -1 p = -1.732050808 + -1 Combine like terms: -1.732050808 + -1 = -2.732050808 p = -2.732050808 Simplifying p = -2.732050808Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.732050808, -2.732050808}Solution
p = {0.732050808, -2.732050808}
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