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Simplifying 2p2 + 12p + -12 = 0 Reorder the terms: -12 + 12p + 2p2 = 0 Solving -12 + 12p + 2p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + 6p + p2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + 6p + p2)' equal to zero and attempt to solve: Simplifying -6 + 6p + p2 = 0 Solving -6 + 6p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + 6p + 6 + p2 = 0 + 6 Reorder the terms: -6 + 6 + 6p + p2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 6p + p2 = 0 + 6 6p + p2 = 0 + 6 Combine like terms: 0 + 6 = 6 6p + p2 = 6 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 = 6 + 9 Reorder the terms: 9 + 6p + p2 = 6 + 9 Combine like terms: 6 + 9 = 15 9 + 6p + p2 = 15 Factor a perfect square on the left side: (p + 3)(p + 3) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (p + 3) equal to 3.872983346 and -3.872983346.Subproblem 1
p + 3 = 3.872983346 Simplifying p + 3 = 3.872983346 Reorder the terms: 3 + p = 3.872983346 Solving 3 + p = 3.872983346 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 = 3.872983346 + -3 Combine like terms: 3 + -3 = 0 0 + p = 3.872983346 + -3 p = 3.872983346 + -3 Combine like terms: 3.872983346 + -3 = 0.872983346 p = 0.872983346 Simplifying p = 0.872983346Subproblem 2
p + 3 = -3.872983346 Simplifying p + 3 = -3.872983346 Reorder the terms: 3 + p = -3.872983346 Solving 3 + p = -3.872983346 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 = -3.872983346 + -3 Combine like terms: 3 + -3 = 0 0 + p = -3.872983346 + -3 p = -3.872983346 + -3 Combine like terms: -3.872983346 + -3 = -6.872983346 p = -6.872983346 Simplifying p = -6.872983346Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.872983346, -6.872983346}Solution
p = {0.872983346, -6.872983346}
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