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Simplifying 4 = 2 + -5p + p2 Solving 4 = 2 + -5p + p2 Solving for variable 'p'. Combine like terms: 4 + -2 = 2 2 + 5p + -1p2 = 2 + -5p + p2 + -2 + 5p + -1p2 Reorder the terms: 2 + 5p + -1p2 = 2 + -2 + -5p + 5p + p2 + -1p2 Combine like terms: 2 + -2 = 0 2 + 5p + -1p2 = 0 + -5p + 5p + p2 + -1p2 2 + 5p + -1p2 = -5p + 5p + p2 + -1p2 Combine like terms: -5p + 5p = 0 2 + 5p + -1p2 = 0 + p2 + -1p2 2 + 5p + -1p2 = p2 + -1p2 Combine like terms: p2 + -1p2 = 0 2 + 5p + -1p2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2 + -5p + p2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -5p + 2 + p2 = 0 + 2 Reorder the terms: -2 + 2 + -5p + p2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -5p + p2 = 0 + 2 -5p + p2 = 0 + 2 Combine like terms: 0 + 2 = 2 -5p + p2 = 2 The p term is -5p. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5p + 6.25 + p2 = 2 + 6.25 Reorder the terms: 6.25 + -5p + p2 = 2 + 6.25 Combine like terms: 2 + 6.25 = 8.25 6.25 + -5p + p2 = 8.25 Factor a perfect square on the left side: (p + -2.5)(p + -2.5) = 8.25 Calculate the square root of the right side: 2.872281323 Break this problem into two subproblems by setting (p + -2.5) equal to 2.872281323 and -2.872281323.Subproblem 1
p + -2.5 = 2.872281323 Simplifying p + -2.5 = 2.872281323 Reorder the terms: -2.5 + p = 2.872281323 Solving -2.5 + p = 2.872281323 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + p = 2.872281323 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + p = 2.872281323 + 2.5 p = 2.872281323 + 2.5 Combine like terms: 2.872281323 + 2.5 = 5.372281323 p = 5.372281323 Simplifying p = 5.372281323Subproblem 2
p + -2.5 = -2.872281323 Simplifying p + -2.5 = -2.872281323 Reorder the terms: -2.5 + p = -2.872281323 Solving -2.5 + p = -2.872281323 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + p = -2.872281323 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + p = -2.872281323 + 2.5 p = -2.872281323 + 2.5 Combine like terms: -2.872281323 + 2.5 = -0.372281323 p = -0.372281323 Simplifying p = -0.372281323Solution
The solution to the problem is based on the solutions from the subproblems. p = {5.372281323, -0.372281323}
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