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Simplifying 2p2 + 4p + 20 = 1000 Reorder the terms: 20 + 4p + 2p2 = 1000 Solving 20 + 4p + 2p2 = 1000 Solving for variable 'p'. Reorder the terms: 20 + -1000 + 4p + 2p2 = 1000 + -1000 Combine like terms: 20 + -1000 = -980 -980 + 4p + 2p2 = 1000 + -1000 Combine like terms: 1000 + -1000 = 0 -980 + 4p + 2p2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-490 + 2p + p2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-490 + 2p + p2)' equal to zero and attempt to solve: Simplifying -490 + 2p + p2 = 0 Solving -490 + 2p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '490' to each side of the equation. -490 + 2p + 490 + p2 = 0 + 490 Reorder the terms: -490 + 490 + 2p + p2 = 0 + 490 Combine like terms: -490 + 490 = 0 0 + 2p + p2 = 0 + 490 2p + p2 = 0 + 490 Combine like terms: 0 + 490 = 490 2p + p2 = 490 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 = 490 + 1 Reorder the terms: 1 + 2p + p2 = 490 + 1 Combine like terms: 490 + 1 = 491 1 + 2p + p2 = 491 Factor a perfect square on the left side: (p + 1)(p + 1) = 491 Calculate the square root of the right side: 22.158519806 Break this problem into two subproblems by setting (p + 1) equal to 22.158519806 and -22.158519806.Subproblem 1
p + 1 = 22.158519806 Simplifying p + 1 = 22.158519806 Reorder the terms: 1 + p = 22.158519806 Solving 1 + p = 22.158519806 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 = 22.158519806 + -1 Combine like terms: 1 + -1 = 0 0 + p = 22.158519806 + -1 p = 22.158519806 + -1 Combine like terms: 22.158519806 + -1 = 21.158519806 p = 21.158519806 Simplifying p = 21.158519806Subproblem 2
p + 1 = -22.158519806 Simplifying p + 1 = -22.158519806 Reorder the terms: 1 + p = -22.158519806 Solving 1 + p = -22.158519806 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 = -22.158519806 + -1 Combine like terms: 1 + -1 = 0 0 + p = -22.158519806 + -1 p = -22.158519806 + -1 Combine like terms: -22.158519806 + -1 = -23.158519806 p = -23.158519806 Simplifying p = -23.158519806Solution
The solution to the problem is based on the solutions from the subproblems. p = {21.158519806, -23.158519806}Solution
p = {21.158519806, -23.158519806}
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