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Simplifying p2 + 9p + 2 = 0 Reorder the terms: 2 + 9p + p2 = 0 Solving 2 + 9p + p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + 9p + -2 + p2 = 0 + -2 Reorder the terms: 2 + -2 + 9p + p2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 9p + p2 = 0 + -2 9p + p2 = 0 + -2 Combine like terms: 0 + -2 = -2 9p + p2 = -2 The p term is 9p. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9p + 20.25 + p2 = -2 + 20.25 Reorder the terms: 20.25 + 9p + p2 = -2 + 20.25 Combine like terms: -2 + 20.25 = 18.25 20.25 + 9p + p2 = 18.25 Factor a perfect square on the left side: (p + 4.5)(p + 4.5) = 18.25 Calculate the square root of the right side: 4.272001873 Break this problem into two subproblems by setting (p + 4.5) equal to 4.272001873 and -4.272001873.Subproblem 1
p + 4.5 = 4.272001873 Simplifying p + 4.5 = 4.272001873 Reorder the terms: 4.5 + p = 4.272001873 Solving 4.5 + p = 4.272001873 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + p = 4.272001873 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + p = 4.272001873 + -4.5 p = 4.272001873 + -4.5 Combine like terms: 4.272001873 + -4.5 = -0.227998127 p = -0.227998127 Simplifying p = -0.227998127Subproblem 2
p + 4.5 = -4.272001873 Simplifying p + 4.5 = -4.272001873 Reorder the terms: 4.5 + p = -4.272001873 Solving 4.5 + p = -4.272001873 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + p = -4.272001873 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + p = -4.272001873 + -4.5 p = -4.272001873 + -4.5 Combine like terms: -4.272001873 + -4.5 = -8.772001873 p = -8.772001873 Simplifying p = -8.772001873Solution
The solution to the problem is based on the solutions from the subproblems. p = {-0.227998127, -8.772001873}
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