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Simplifying p2 + -6p + -5 = -8 Reorder the terms: -5 + -6p + p2 = -8 Solving -5 + -6p + p2 = -8 Solving for variable 'p'. Reorder the terms: -5 + 8 + -6p + p2 = -8 + 8 Combine like terms: -5 + 8 = 3 3 + -6p + p2 = -8 + 8 Combine like terms: -8 + 8 = 0 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 = 6 9 + -6p + p2 = 6 Factor a perfect square on the left side: (p + -3)(p + -3) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (p + -3) equal to 2.449489743 and -2.449489743.Subproblem 1
p + -3 = 2.449489743 Simplifying p + -3 = 2.449489743 Reorder the terms: -3 + p = 2.449489743 Solving -3 + p = 2.449489743 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 = 2.449489743 + 3 Combine like terms: -3 + 3 = 0 0 + p = 2.449489743 + 3 p = 2.449489743 + 3 Combine like terms: 2.449489743 + 3 = 5.449489743 p = 5.449489743 Simplifying p = 5.449489743Subproblem 2
p + -3 = -2.449489743 Simplifying p + -3 = -2.449489743 Reorder the terms: -3 + p = -2.449489743 Solving -3 + p = -2.449489743 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 = -2.449489743 + 3 Combine like terms: -3 + 3 = 0 0 + p = -2.449489743 + 3 p = -2.449489743 + 3 Combine like terms: -2.449489743 + 3 = 0.550510257 p = 0.550510257 Simplifying p = 0.550510257Solution
The solution to the problem is based on the solutions from the subproblems. p = {5.449489743, 0.550510257}
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