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Simplifying 3p2 + -18p + -9 = 0 Reorder the terms: -9 + -18p + 3p2 = 0 Solving -9 + -18p + 3p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '3'. 3(-3 + -6p + p2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-3 + -6p + p2)' equal to zero and attempt to solve: Simplifying -3 + -6p + p2 = 0 Solving -3 + -6p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + -6p + 3 + p2 = 0 + 3 Reorder the terms: -3 + 3 + -6p + p2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -6p + p2 = 0 + 3 -6p + p2 = 0 + 3 Combine like terms: 0 + 3 = 3 -6p + p2 = 3 The p term is -6p. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6p + 9 + p2 = 3 + 9 Reorder the terms: 9 + -6p + p2 = 3 + 9 Combine like terms: 3 + 9 = 12 9 + -6p + p2 = 12 Factor a perfect square on the left side: (p + -3)(p + -3) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (p + -3) equal to 3.464101615 and -3.464101615.Subproblem 1
p + -3 = 3.464101615 Simplifying p + -3 = 3.464101615 Reorder the terms: -3 + p = 3.464101615 Solving -3 + p = 3.464101615 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + p = 3.464101615 + 3 Combine like terms: -3 + 3 = 0 0 + p = 3.464101615 + 3 p = 3.464101615 + 3 Combine like terms: 3.464101615 + 3 = 6.464101615 p = 6.464101615 Simplifying p = 6.464101615Subproblem 2
p + -3 = -3.464101615 Simplifying p + -3 = -3.464101615 Reorder the terms: -3 + p = -3.464101615 Solving -3 + p = -3.464101615 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + p = -3.464101615 + 3 Combine like terms: -3 + 3 = 0 0 + p = -3.464101615 + 3 p = -3.464101615 + 3 Combine like terms: -3.464101615 + 3 = -0.464101615 p = -0.464101615 Simplifying p = -0.464101615Solution
The solution to the problem is based on the solutions from the subproblems. p = {6.464101615, -0.464101615}Solution
p = {6.464101615, -0.464101615}
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