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Simplifying 3p2 + -27p + 33 = 0 Reorder the terms: 33 + -27p + 3p2 = 0 Solving 33 + -27p + 3p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '3'. 3(11 + -9p + p2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(11 + -9p + p2)' equal to zero and attempt to solve: Simplifying 11 + -9p + p2 = 0 Solving 11 + -9p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '-11' to each side of the equation. 11 + -9p + -11 + p2 = 0 + -11 Reorder the terms: 11 + -11 + -9p + p2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -9p + p2 = 0 + -11 -9p + p2 = 0 + -11 Combine like terms: 0 + -11 = -11 -9p + p2 = -11 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 = -11 + 20.25 Reorder the terms: 20.25 + -9p + p2 = -11 + 20.25 Combine like terms: -11 + 20.25 = 9.25 20.25 + -9p + p2 = 9.25 Factor a perfect square on the left side: (p + -4.5)(p + -4.5) = 9.25 Calculate the square root of the right side: 3.041381265 Break this problem into two subproblems by setting (p + -4.5) equal to 3.041381265 and -3.041381265.Subproblem 1
p + -4.5 = 3.041381265 Simplifying p + -4.5 = 3.041381265 Reorder the terms: -4.5 + p = 3.041381265 Solving -4.5 + p = 3.041381265 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 = 3.041381265 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + p = 3.041381265 + 4.5 p = 3.041381265 + 4.5 Combine like terms: 3.041381265 + 4.5 = 7.541381265 p = 7.541381265 Simplifying p = 7.541381265Subproblem 2
p + -4.5 = -3.041381265 Simplifying p + -4.5 = -3.041381265 Reorder the terms: -4.5 + p = -3.041381265 Solving -4.5 + p = -3.041381265 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 = -3.041381265 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + p = -3.041381265 + 4.5 p = -3.041381265 + 4.5 Combine like terms: -3.041381265 + 4.5 = 1.458618735 p = 1.458618735 Simplifying p = 1.458618735Solution
The solution to the problem is based on the solutions from the subproblems. p = {7.541381265, 1.458618735}Solution
p = {7.541381265, 1.458618735}
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