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Simplifying p2 + 17p + -48 = 0 Reorder the terms: -48 + 17p + p2 = 0 Solving -48 + 17p + p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '48' to each side of the equation. -48 + 17p + 48 + p2 = 0 + 48 Reorder the terms: -48 + 48 + 17p + p2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + 17p + p2 = 0 + 48 17p + p2 = 0 + 48 Combine like terms: 0 + 48 = 48 17p + p2 = 48 The p term is 17p. Take half its coefficient (8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. 17p + 72.25 + p2 = 48 + 72.25 Reorder the terms: 72.25 + 17p + p2 = 48 + 72.25 Combine like terms: 48 + 72.25 = 120.25 72.25 + 17p + p2 = 120.25 Factor a perfect square on the left side: (p + 8.5)(p + 8.5) = 120.25 Calculate the square root of the right side: 10.9658561 Break this problem into two subproblems by setting (p + 8.5) equal to 10.9658561 and -10.9658561.Subproblem 1
p + 8.5 = 10.9658561 Simplifying p + 8.5 = 10.9658561 Reorder the terms: 8.5 + p = 10.9658561 Solving 8.5 + p = 10.9658561 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + p = 10.9658561 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + p = 10.9658561 + -8.5 p = 10.9658561 + -8.5 Combine like terms: 10.9658561 + -8.5 = 2.4658561 p = 2.4658561 Simplifying p = 2.4658561Subproblem 2
p + 8.5 = -10.9658561 Simplifying p + 8.5 = -10.9658561 Reorder the terms: 8.5 + p = -10.9658561 Solving 8.5 + p = -10.9658561 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + p = -10.9658561 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + p = -10.9658561 + -8.5 p = -10.9658561 + -8.5 Combine like terms: -10.9658561 + -8.5 = -19.4658561 p = -19.4658561 Simplifying p = -19.4658561Solution
The solution to the problem is based on the solutions from the subproblems. p = {2.4658561, -19.4658561}
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