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Simplifying p2 + 4p + -256 = 0 Reorder the terms: -256 + 4p + p2 = 0 Solving -256 + 4p + p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '256' to each side of the equation. -256 + 4p + 256 + p2 = 0 + 256 Reorder the terms: -256 + 256 + 4p + p2 = 0 + 256 Combine like terms: -256 + 256 = 0 0 + 4p + p2 = 0 + 256 4p + p2 = 0 + 256 Combine like terms: 0 + 256 = 256 4p + p2 = 256 The p term is 4p. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4p + 4 + p2 = 256 + 4 Reorder the terms: 4 + 4p + p2 = 256 + 4 Combine like terms: 256 + 4 = 260 4 + 4p + p2 = 260 Factor a perfect square on the left side: (p + 2)(p + 2) = 260 Calculate the square root of the right side: 16.124515497 Break this problem into two subproblems by setting (p + 2) equal to 16.124515497 and -16.124515497.Subproblem 1
p + 2 = 16.124515497 Simplifying p + 2 = 16.124515497 Reorder the terms: 2 + p = 16.124515497 Solving 2 + p = 16.124515497 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + p = 16.124515497 + -2 Combine like terms: 2 + -2 = 0 0 + p = 16.124515497 + -2 p = 16.124515497 + -2 Combine like terms: 16.124515497 + -2 = 14.124515497 p = 14.124515497 Simplifying p = 14.124515497Subproblem 2
p + 2 = -16.124515497 Simplifying p + 2 = -16.124515497 Reorder the terms: 2 + p = -16.124515497 Solving 2 + p = -16.124515497 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + p = -16.124515497 + -2 Combine like terms: 2 + -2 = 0 0 + p = -16.124515497 + -2 p = -16.124515497 + -2 Combine like terms: -16.124515497 + -2 = -18.124515497 p = -18.124515497 Simplifying p = -18.124515497Solution
The solution to the problem is based on the solutions from the subproblems. p = {14.124515497, -18.124515497}
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