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Simplifying 9p2 + 36p = 17 Reorder the terms: 36p + 9p2 = 17 Solving 36p + 9p2 = 17 Solving for variable 'p'. Reorder the terms: -17 + 36p + 9p2 = 17 + -17 Combine like terms: 17 + -17 = 0 -17 + 36p + 9p2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.888888889 + 4p + p2 = 0 Move the constant term to the right: Add '1.888888889' to each side of the equation. -1.888888889 + 4p + 1.888888889 + p2 = 0 + 1.888888889 Reorder the terms: -1.888888889 + 1.888888889 + 4p + p2 = 0 + 1.888888889 Combine like terms: -1.888888889 + 1.888888889 = 0.000000000 0.000000000 + 4p + p2 = 0 + 1.888888889 4p + p2 = 0 + 1.888888889 Combine like terms: 0 + 1.888888889 = 1.888888889 4p + p2 = 1.888888889 The p term is 4p. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4p + 4 + p2 = 1.888888889 + 4 Reorder the terms: 4 + 4p + p2 = 1.888888889 + 4 Combine like terms: 1.888888889 + 4 = 5.888888889 4 + 4p + p2 = 5.888888889 Factor a perfect square on the left side: (p + 2)(p + 2) = 5.888888889 Calculate the square root of the right side: 2.426703296 Break this problem into two subproblems by setting (p + 2) equal to 2.426703296 and -2.426703296.Subproblem 1
p + 2 = 2.426703296 Simplifying p + 2 = 2.426703296 Reorder the terms: 2 + p = 2.426703296 Solving 2 + p = 2.426703296 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + p = 2.426703296 + -2 Combine like terms: 2 + -2 = 0 0 + p = 2.426703296 + -2 p = 2.426703296 + -2 Combine like terms: 2.426703296 + -2 = 0.426703296 p = 0.426703296 Simplifying p = 0.426703296Subproblem 2
p + 2 = -2.426703296 Simplifying p + 2 = -2.426703296 Reorder the terms: 2 + p = -2.426703296 Solving 2 + p = -2.426703296 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + p = -2.426703296 + -2 Combine like terms: 2 + -2 = 0 0 + p = -2.426703296 + -2 p = -2.426703296 + -2 Combine like terms: -2.426703296 + -2 = -4.426703296 p = -4.426703296 Simplifying p = -4.426703296Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.426703296, -4.426703296}
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