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Simplifying 3p2 + 9p = 18 Reorder the terms: 9p + 3p2 = 18 Solving 9p + 3p2 = 18 Solving for variable 'p'. Reorder the terms: -18 + 9p + 3p2 = 18 + -18 Combine like terms: 18 + -18 = 0 -18 + 9p + 3p2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-6 + 3p + p2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-6 + 3p + p2)' equal to zero and attempt to solve: Simplifying -6 + 3p + p2 = 0 Solving -6 + 3p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + 3p + 6 + p2 = 0 + 6 Reorder the terms: -6 + 6 + 3p + p2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 3p + p2 = 0 + 6 3p + p2 = 0 + 6 Combine like terms: 0 + 6 = 6 3p + p2 = 6 The p term is 3p. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3p + 2.25 + p2 = 6 + 2.25 Reorder the terms: 2.25 + 3p + p2 = 6 + 2.25 Combine like terms: 6 + 2.25 = 8.25 2.25 + 3p + p2 = 8.25 Factor a perfect square on the left side: (p + 1.5)(p + 1.5) = 8.25 Calculate the square root of the right side: 2.872281323 Break this problem into two subproblems by setting (p + 1.5) equal to 2.872281323 and -2.872281323.Subproblem 1
p + 1.5 = 2.872281323 Simplifying p + 1.5 = 2.872281323 Reorder the terms: 1.5 + p = 2.872281323 Solving 1.5 + p = 2.872281323 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + p = 2.872281323 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + p = 2.872281323 + -1.5 p = 2.872281323 + -1.5 Combine like terms: 2.872281323 + -1.5 = 1.372281323 p = 1.372281323 Simplifying p = 1.372281323Subproblem 2
p + 1.5 = -2.872281323 Simplifying p + 1.5 = -2.872281323 Reorder the terms: 1.5 + p = -2.872281323 Solving 1.5 + p = -2.872281323 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + p = -2.872281323 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + p = -2.872281323 + -1.5 p = -2.872281323 + -1.5 Combine like terms: -2.872281323 + -1.5 = -4.372281323 p = -4.372281323 Simplifying p = -4.372281323Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.372281323, -4.372281323}Solution
p = {1.372281323, -4.372281323}
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