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Simplifying p + -1p2 = 0.082323 Solving p + -1p2 = 0.082323 Solving for variable 'p'. Reorder the terms: -0.082323 + p + -1p2 = 0.082323 + -0.082323 Combine like terms: 0.082323 + -0.082323 = 0.000000 -0.082323 + p + -1p2 = 0.000000 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 0.082323 + -1p + p2 = 0.000000 Move the constant term to the right: Add '-0.082323' to each side of the equation. 0.082323 + -1p + -0.082323 + p2 = 0.000000 + -0.082323 Reorder the terms: 0.082323 + -0.082323 + -1p + p2 = 0.000000 + -0.082323 Combine like terms: 0.082323 + -0.082323 = 0.000000 0.000000 + -1p + p2 = 0.000000 + -0.082323 -1p + p2 = 0.000000 + -0.082323 Combine like terms: 0.000000 + -0.082323 = -0.082323 -1p + p2 = -0.082323 The p term is p. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1p + 0.25 + p2 = -0.082323 + 0.25 Reorder the terms: 0.25 + -1p + p2 = -0.082323 + 0.25 Combine like terms: -0.082323 + 0.25 = 0.167677 0.25 + -1p + p2 = 0.167677 Factor a perfect square on the left side: (p + 0.5)(p + 0.5) = 0.167677 Calculate the square root of the right side: 0.409483821 Break this problem into two subproblems by setting (p + 0.5) equal to 0.409483821 and -0.409483821.Subproblem 1
p + 0.5 = 0.409483821 Simplifying p + 0.5 = 0.409483821 Reorder the terms: 0.5 + p = 0.409483821 Solving 0.5 + p = 0.409483821 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + p = 0.409483821 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + p = 0.409483821 + -0.5 p = 0.409483821 + -0.5 Combine like terms: 0.409483821 + -0.5 = -0.090516179 p = -0.090516179 Simplifying p = -0.090516179Subproblem 2
p + 0.5 = -0.409483821 Simplifying p + 0.5 = -0.409483821 Reorder the terms: 0.5 + p = -0.409483821 Solving 0.5 + p = -0.409483821 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + p = -0.409483821 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + p = -0.409483821 + -0.5 p = -0.409483821 + -0.5 Combine like terms: -0.409483821 + -0.5 = -0.909483821 p = -0.909483821 Simplifying p = -0.909483821Solution
The solution to the problem is based on the solutions from the subproblems. p = {-0.090516179, -0.909483821}
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