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Simplifying 4p(p + 9) = 3 Reorder the terms: 4p(9 + p) = 3 (9 * 4p + p * 4p) = 3 (36p + 4p2) = 3 Solving 36p + 4p2 = 3 Solving for variable 'p'. Reorder the terms: -3 + 36p + 4p2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + 36p + 4p2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.75 + 9p + p2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + 9p + 0.75 + p2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + 9p + p2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + 9p + p2 = 0 + 0.75 9p + p2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 9p + p2 = 0.75 The p term is 9p. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9p + 20.25 + p2 = 0.75 + 20.25 Reorder the terms: 20.25 + 9p + p2 = 0.75 + 20.25 Combine like terms: 0.75 + 20.25 = 21 20.25 + 9p + p2 = 21 Factor a perfect square on the left side: (p + 4.5)(p + 4.5) = 21 Calculate the square root of the right side: 4.582575695 Break this problem into two subproblems by setting (p + 4.5) equal to 4.582575695 and -4.582575695.Subproblem 1
p + 4.5 = 4.582575695 Simplifying p + 4.5 = 4.582575695 Reorder the terms: 4.5 + p = 4.582575695 Solving 4.5 + p = 4.582575695 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + p = 4.582575695 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + p = 4.582575695 + -4.5 p = 4.582575695 + -4.5 Combine like terms: 4.582575695 + -4.5 = 0.082575695 p = 0.082575695 Simplifying p = 0.082575695Subproblem 2
p + 4.5 = -4.582575695 Simplifying p + 4.5 = -4.582575695 Reorder the terms: 4.5 + p = -4.582575695 Solving 4.5 + p = -4.582575695 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + p = -4.582575695 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + p = -4.582575695 + -4.5 p = -4.582575695 + -4.5 Combine like terms: -4.582575695 + -4.5 = -9.082575695 p = -9.082575695 Simplifying p = -9.082575695Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.082575695, -9.082575695}
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