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Simplifying p2 + 6p + 9 = 18 Reorder the terms: 9 + 6p + p2 = 18 Solving 9 + 6p + p2 = 18 Solving for variable 'p'. Reorder the terms: 9 + -18 + 6p + p2 = 18 + -18 Combine like terms: 9 + -18 = -9 -9 + 6p + p2 = 18 + -18 Combine like terms: 18 + -18 = 0 -9 + 6p + p2 = 0 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 = 1.242640687 p = 1.242640687 Simplifying p = 1.242640687Subproblem 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 = -7.242640687 p = -7.242640687 Simplifying p = -7.242640687Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.242640687, -7.242640687}
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