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Simplifying p2 + 25 + -16p = 0 Reorder the terms: 25 + -16p + p2 = 0 Solving 25 + -16p + p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '-25' to each side of the equation. 25 + -16p + -25 + p2 = 0 + -25 Reorder the terms: 25 + -25 + -16p + p2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -16p + p2 = 0 + -25 -16p + p2 = 0 + -25 Combine like terms: 0 + -25 = -25 -16p + p2 = -25 The p term is -16p. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16p + 64 + p2 = -25 + 64 Reorder the terms: 64 + -16p + p2 = -25 + 64 Combine like terms: -25 + 64 = 39 64 + -16p + p2 = 39 Factor a perfect square on the left side: (p + -8)(p + -8) = 39 Calculate the square root of the right side: 6.244997998 Break this problem into two subproblems by setting (p + -8) equal to 6.244997998 and -6.244997998.Subproblem 1
p + -8 = 6.244997998 Simplifying p + -8 = 6.244997998 Reorder the terms: -8 + p = 6.244997998 Solving -8 + p = 6.244997998 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + p = 6.244997998 + 8 Combine like terms: -8 + 8 = 0 0 + p = 6.244997998 + 8 p = 6.244997998 + 8 Combine like terms: 6.244997998 + 8 = 14.244997998 p = 14.244997998 Simplifying p = 14.244997998Subproblem 2
p + -8 = -6.244997998 Simplifying p + -8 = -6.244997998 Reorder the terms: -8 + p = -6.244997998 Solving -8 + p = -6.244997998 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + p = -6.244997998 + 8 Combine like terms: -8 + 8 = 0 0 + p = -6.244997998 + 8 p = -6.244997998 + 8 Combine like terms: -6.244997998 + 8 = 1.755002002 p = 1.755002002 Simplifying p = 1.755002002Solution
The solution to the problem is based on the solutions from the subproblems. p = {14.244997998, 1.755002002}
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