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Simplifying (p + -3)(p + -3) + -18 = 0 Reorder the terms: (-3 + p)(p + -3) + -18 = 0 Reorder the terms: (-3 + p)(-3 + p) + -18 = 0 Multiply (-3 + p) * (-3 + p) (-3(-3 + p) + p(-3 + p)) + -18 = 0 ((-3 * -3 + p * -3) + p(-3 + p)) + -18 = 0 ((9 + -3p) + p(-3 + p)) + -18 = 0 (9 + -3p + (-3 * p + p * p)) + -18 = 0 (9 + -3p + (-3p + p2)) + -18 = 0 Combine like terms: -3p + -3p = -6p (9 + -6p + p2) + -18 = 0 Reorder the terms: 9 + -18 + -6p + p2 = 0 Combine like terms: 9 + -18 = -9 -9 + -6p + p2 = 0 Solving -9 + -6p + p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + -6p + 9 + p2 = 0 + 9 Reorder the terms: -9 + 9 + -6p + p2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -6p + p2 = 0 + 9 -6p + p2 = 0 + 9 Combine like terms: 0 + 9 = 9 -6p + p2 = 9 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 = 9 + 9 Reorder the terms: 9 + -6p + p2 = 9 + 9 Combine like terms: 9 + 9 = 18 9 + -6p + p2 = 18 Factor a perfect square on the left side: (p + -3)(p + -3) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (p + -3) equal to 4.242640687 and -4.242640687.Subproblem 1
p + -3 = 4.242640687 Simplifying p + -3 = 4.242640687 Reorder the terms: -3 + p = 4.242640687 Solving -3 + p = 4.242640687 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 = 4.242640687 + 3 Combine like terms: -3 + 3 = 0 0 + p = 4.242640687 + 3 p = 4.242640687 + 3 Combine like terms: 4.242640687 + 3 = 7.242640687 p = 7.242640687 Simplifying p = 7.242640687Subproblem 2
p + -3 = -4.242640687 Simplifying p + -3 = -4.242640687 Reorder the terms: -3 + p = -4.242640687 Solving -3 + p = -4.242640687 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 = -4.242640687 + 3 Combine like terms: -3 + 3 = 0 0 + p = -4.242640687 + 3 p = -4.242640687 + 3 Combine like terms: -4.242640687 + 3 = -1.242640687 p = -1.242640687 Simplifying p = -1.242640687Solution
The solution to the problem is based on the solutions from the subproblems. p = {7.242640687, -1.242640687}
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