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Simplifying 4 = -1(p2 + 7p) Reorder the terms: 4 = -1(7p + p2) 4 = (7p * -1 + p2 * -1) 4 = (-7p + -1p2) Solving 4 = -7p + -1p2 Solving for variable 'p'. Reorder the terms: 4 + 7p + p2 = -7p + 7p + -1p2 + p2 Combine like terms: -7p + 7p = 0 4 + 7p + p2 = 0 + -1p2 + p2 4 + 7p + p2 = -1p2 + p2 Combine like terms: -1p2 + p2 = 0 4 + 7p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + 7p + -4 + p2 = 0 + -4 Reorder the terms: 4 + -4 + 7p + p2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 7p + p2 = 0 + -4 7p + p2 = 0 + -4 Combine like terms: 0 + -4 = -4 7p + p2 = -4 The p term is 7p. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7p + 12.25 + p2 = -4 + 12.25 Reorder the terms: 12.25 + 7p + p2 = -4 + 12.25 Combine like terms: -4 + 12.25 = 8.25 12.25 + 7p + p2 = 8.25 Factor a perfect square on the left side: (p + 3.5)(p + 3.5) = 8.25 Calculate the square root of the right side: 2.872281323 Break this problem into two subproblems by setting (p + 3.5) equal to 2.872281323 and -2.872281323.Subproblem 1
p + 3.5 = 2.872281323 Simplifying p + 3.5 = 2.872281323 Reorder the terms: 3.5 + p = 2.872281323 Solving 3.5 + p = 2.872281323 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + p = 2.872281323 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + p = 2.872281323 + -3.5 p = 2.872281323 + -3.5 Combine like terms: 2.872281323 + -3.5 = -0.627718677 p = -0.627718677 Simplifying p = -0.627718677Subproblem 2
p + 3.5 = -2.872281323 Simplifying p + 3.5 = -2.872281323 Reorder the terms: 3.5 + p = -2.872281323 Solving 3.5 + p = -2.872281323 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + p = -2.872281323 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + p = -2.872281323 + -3.5 p = -2.872281323 + -3.5 Combine like terms: -2.872281323 + -3.5 = -6.372281323 p = -6.372281323 Simplifying p = -6.372281323Solution
The solution to the problem is based on the solutions from the subproblems. p = {-0.627718677, -6.372281323}
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