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Simplifying 3p2 + -28 = 27p Reorder the terms: -28 + 3p2 = 27p Solving -28 + 3p2 = 27p Solving for variable 'p'. Reorder the terms: -28 + -27p + 3p2 = 27p + -27p Combine like terms: 27p + -27p = 0 -28 + -27p + 3p2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -9.333333333 + -9p + p2 = 0 Move the constant term to the right: Add '9.333333333' to each side of the equation. -9.333333333 + -9p + 9.333333333 + p2 = 0 + 9.333333333 Reorder the terms: -9.333333333 + 9.333333333 + -9p + p2 = 0 + 9.333333333 Combine like terms: -9.333333333 + 9.333333333 = 0.000000000 0.000000000 + -9p + p2 = 0 + 9.333333333 -9p + p2 = 0 + 9.333333333 Combine like terms: 0 + 9.333333333 = 9.333333333 -9p + p2 = 9.333333333 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 = 9.333333333 + 20.25 Reorder the terms: 20.25 + -9p + p2 = 9.333333333 + 20.25 Combine like terms: 9.333333333 + 20.25 = 29.583333333 20.25 + -9p + p2 = 29.583333333 Factor a perfect square on the left side: (p + -4.5)(p + -4.5) = 29.583333333 Calculate the square root of the right side: 5.439056291 Break this problem into two subproblems by setting (p + -4.5) equal to 5.439056291 and -5.439056291.Subproblem 1
p + -4.5 = 5.439056291 Simplifying p + -4.5 = 5.439056291 Reorder the terms: -4.5 + p = 5.439056291 Solving -4.5 + p = 5.439056291 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 = 5.439056291 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + p = 5.439056291 + 4.5 p = 5.439056291 + 4.5 Combine like terms: 5.439056291 + 4.5 = 9.939056291 p = 9.939056291 Simplifying p = 9.939056291Subproblem 2
p + -4.5 = -5.439056291 Simplifying p + -4.5 = -5.439056291 Reorder the terms: -4.5 + p = -5.439056291 Solving -4.5 + p = -5.439056291 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 = -5.439056291 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + p = -5.439056291 + 4.5 p = -5.439056291 + 4.5 Combine like terms: -5.439056291 + 4.5 = -0.939056291 p = -0.939056291 Simplifying p = -0.939056291Solution
The solution to the problem is based on the solutions from the subproblems. p = {9.939056291, -0.939056291}
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