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Simplifying p2 + 8p = 97 Reorder the terms: 8p + p2 = 97 Solving 8p + p2 = 97 Solving for variable 'p'. Reorder the terms: -97 + 8p + p2 = 97 + -97 Combine like terms: 97 + -97 = 0 -97 + 8p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '97' to each side of the equation. -97 + 8p + 97 + p2 = 0 + 97 Reorder the terms: -97 + 97 + 8p + p2 = 0 + 97 Combine like terms: -97 + 97 = 0 0 + 8p + p2 = 0 + 97 8p + p2 = 0 + 97 Combine like terms: 0 + 97 = 97 8p + p2 = 97 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 = 97 + 16 Reorder the terms: 16 + 8p + p2 = 97 + 16 Combine like terms: 97 + 16 = 113 16 + 8p + p2 = 113 Factor a perfect square on the left side: (p + 4)(p + 4) = 113 Calculate the square root of the right side: 10.630145813 Break this problem into two subproblems by setting (p + 4) equal to 10.630145813 and -10.630145813.Subproblem 1
p + 4 = 10.630145813 Simplifying p + 4 = 10.630145813 Reorder the terms: 4 + p = 10.630145813 Solving 4 + p = 10.630145813 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 = 10.630145813 + -4 Combine like terms: 4 + -4 = 0 0 + p = 10.630145813 + -4 p = 10.630145813 + -4 Combine like terms: 10.630145813 + -4 = 6.630145813 p = 6.630145813 Simplifying p = 6.630145813Subproblem 2
p + 4 = -10.630145813 Simplifying p + 4 = -10.630145813 Reorder the terms: 4 + p = -10.630145813 Solving 4 + p = -10.630145813 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 = -10.630145813 + -4 Combine like terms: 4 + -4 = 0 0 + p = -10.630145813 + -4 p = -10.630145813 + -4 Combine like terms: -10.630145813 + -4 = -14.630145813 p = -14.630145813 Simplifying p = -14.630145813Solution
The solution to the problem is based on the solutions from the subproblems. p = {6.630145813, -14.630145813}
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