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Simplifying p2 + 6p + -17 = 0 Reorder the terms: -17 + 6p + p2 = 0 Solving -17 + 6p + p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '17' to each side of the equation. -17 + 6p + 17 + p2 = 0 + 17 Reorder the terms: -17 + 17 + 6p + p2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + 6p + p2 = 0 + 17 6p + p2 = 0 + 17 Combine like terms: 0 + 17 = 17 6p + p2 = 17 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 = 17 + 9 Reorder the terms: 9 + 6p + p2 = 17 + 9 Combine like terms: 17 + 9 = 26 9 + 6p + p2 = 26 Factor a perfect square on the left side: (p + 3)(p + 3) = 26 Calculate the square root of the right side: 5.099019514 Break this problem into two subproblems by setting (p + 3) equal to 5.099019514 and -5.099019514.Subproblem 1
p + 3 = 5.099019514 Simplifying p + 3 = 5.099019514 Reorder the terms: 3 + p = 5.099019514 Solving 3 + p = 5.099019514 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 = 5.099019514 + -3 Combine like terms: 3 + -3 = 0 0 + p = 5.099019514 + -3 p = 5.099019514 + -3 Combine like terms: 5.099019514 + -3 = 2.099019514 p = 2.099019514 Simplifying p = 2.099019514Subproblem 2
p + 3 = -5.099019514 Simplifying p + 3 = -5.099019514 Reorder the terms: 3 + p = -5.099019514 Solving 3 + p = -5.099019514 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 = -5.099019514 + -3 Combine like terms: 3 + -3 = 0 0 + p = -5.099019514 + -3 p = -5.099019514 + -3 Combine like terms: -5.099019514 + -3 = -8.099019514 p = -8.099019514 Simplifying p = -8.099019514Solution
The solution to the problem is based on the solutions from the subproblems. p = {2.099019514, -8.099019514}
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