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Simplifying 9p2 + 54p = 13 Reorder the terms: 54p + 9p2 = 13 Solving 54p + 9p2 = 13 Solving for variable 'p'. Reorder the terms: -13 + 54p + 9p2 = 13 + -13 Combine like terms: 13 + -13 = 0 -13 + 54p + 9p2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.444444444 + 6p + p2 = 0 Move the constant term to the right: Add '1.444444444' to each side of the equation. -1.444444444 + 6p + 1.444444444 + p2 = 0 + 1.444444444 Reorder the terms: -1.444444444 + 1.444444444 + 6p + p2 = 0 + 1.444444444 Combine like terms: -1.444444444 + 1.444444444 = 0.000000000 0.000000000 + 6p + p2 = 0 + 1.444444444 6p + p2 = 0 + 1.444444444 Combine like terms: 0 + 1.444444444 = 1.444444444 6p + p2 = 1.444444444 The p term is 6p. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6p + 9 + p2 = 1.444444444 + 9 Reorder the terms: 9 + 6p + p2 = 1.444444444 + 9 Combine like terms: 1.444444444 + 9 = 10.444444444 9 + 6p + p2 = 10.444444444 Factor a perfect square on the left side: (p + 3)(p + 3) = 10.444444444 Calculate the square root of the right side: 3.231786572 Break this problem into two subproblems by setting (p + 3) equal to 3.231786572 and -3.231786572.Subproblem 1
p + 3 = 3.231786572 Simplifying p + 3 = 3.231786572 Reorder the terms: 3 + p = 3.231786572 Solving 3 + p = 3.231786572 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + p = 3.231786572 + -3 Combine like terms: 3 + -3 = 0 0 + p = 3.231786572 + -3 p = 3.231786572 + -3 Combine like terms: 3.231786572 + -3 = 0.231786572 p = 0.231786572 Simplifying p = 0.231786572Subproblem 2
p + 3 = -3.231786572 Simplifying p + 3 = -3.231786572 Reorder the terms: 3 + p = -3.231786572 Solving 3 + p = -3.231786572 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + p = -3.231786572 + -3 Combine like terms: 3 + -3 = 0 0 + p = -3.231786572 + -3 p = -3.231786572 + -3 Combine like terms: -3.231786572 + -3 = -6.231786572 p = -6.231786572 Simplifying p = -6.231786572Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.231786572, -6.231786572}
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