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Simplifying 8p2 + 22p + -9 = 0 Reorder the terms: -9 + 22p + 8p2 = 0 Solving -9 + 22p + 8p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.125 + 2.75p + p2 = 0 Move the constant term to the right: Add '1.125' to each side of the equation. -1.125 + 2.75p + 1.125 + p2 = 0 + 1.125 Reorder the terms: -1.125 + 1.125 + 2.75p + p2 = 0 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + 2.75p + p2 = 0 + 1.125 2.75p + p2 = 0 + 1.125 Combine like terms: 0 + 1.125 = 1.125 2.75p + p2 = 1.125 The p term is 2.75p. Take half its coefficient (1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. 2.75p + 1.890625 + p2 = 1.125 + 1.890625 Reorder the terms: 1.890625 + 2.75p + p2 = 1.125 + 1.890625 Combine like terms: 1.125 + 1.890625 = 3.015625 1.890625 + 2.75p + p2 = 3.015625 Factor a perfect square on the left side: (p + 1.375)(p + 1.375) = 3.015625 Calculate the square root of the right side: 1.736555499 Break this problem into two subproblems by setting (p + 1.375) equal to 1.736555499 and -1.736555499.Subproblem 1
p + 1.375 = 1.736555499 Simplifying p + 1.375 = 1.736555499 Reorder the terms: 1.375 + p = 1.736555499 Solving 1.375 + p = 1.736555499 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-1.375' to each side of the equation. 1.375 + -1.375 + p = 1.736555499 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + p = 1.736555499 + -1.375 p = 1.736555499 + -1.375 Combine like terms: 1.736555499 + -1.375 = 0.361555499 p = 0.361555499 Simplifying p = 0.361555499Subproblem 2
p + 1.375 = -1.736555499 Simplifying p + 1.375 = -1.736555499 Reorder the terms: 1.375 + p = -1.736555499 Solving 1.375 + p = -1.736555499 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-1.375' to each side of the equation. 1.375 + -1.375 + p = -1.736555499 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + p = -1.736555499 + -1.375 p = -1.736555499 + -1.375 Combine like terms: -1.736555499 + -1.375 = -3.111555499 p = -3.111555499 Simplifying p = -3.111555499Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.361555499, -3.111555499}
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