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Simplifying p2 + 8p + -18 = 10 Reorder the terms: -18 + 8p + p2 = 10 Solving -18 + 8p + p2 = 10 Solving for variable 'p'. Reorder the terms: -18 + -10 + 8p + p2 = 10 + -10 Combine like terms: -18 + -10 = -28 -28 + 8p + p2 = 10 + -10 Combine like terms: 10 + -10 = 0 -28 + 8p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '28' to each side of the equation. -28 + 8p + 28 + p2 = 0 + 28 Reorder the terms: -28 + 28 + 8p + p2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + 8p + p2 = 0 + 28 8p + p2 = 0 + 28 Combine like terms: 0 + 28 = 28 8p + p2 = 28 The p term is 8p. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8p + 16 + p2 = 28 + 16 Reorder the terms: 16 + 8p + p2 = 28 + 16 Combine like terms: 28 + 16 = 44 16 + 8p + p2 = 44 Factor a perfect square on the left side: (p + 4)(p + 4) = 44 Calculate the square root of the right side: 6.633249581 Break this problem into two subproblems by setting (p + 4) equal to 6.633249581 and -6.633249581.Subproblem 1
p + 4 = 6.633249581 Simplifying p + 4 = 6.633249581 Reorder the terms: 4 + p = 6.633249581 Solving 4 + p = 6.633249581 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + p = 6.633249581 + -4 Combine like terms: 4 + -4 = 0 0 + p = 6.633249581 + -4 p = 6.633249581 + -4 Combine like terms: 6.633249581 + -4 = 2.633249581 p = 2.633249581 Simplifying p = 2.633249581Subproblem 2
p + 4 = -6.633249581 Simplifying p + 4 = -6.633249581 Reorder the terms: 4 + p = -6.633249581 Solving 4 + p = -6.633249581 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + p = -6.633249581 + -4 Combine like terms: 4 + -4 = 0 0 + p = -6.633249581 + -4 p = -6.633249581 + -4 Combine like terms: -6.633249581 + -4 = -10.633249581 p = -10.633249581 Simplifying p = -10.633249581Solution
The solution to the problem is based on the solutions from the subproblems. p = {2.633249581, -10.633249581}
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