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Simplifying (p2) + 8p = 6 p2 + 8p = 6 Reorder the terms: 8p + p2 = 6 Solving 8p + p2 = 6 Solving for variable 'p'. Reorder the terms: -6 + 8p + p2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + 8p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + 8p + 6 + p2 = 0 + 6 Reorder the terms: -6 + 6 + 8p + p2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 8p + p2 = 0 + 6 8p + p2 = 0 + 6 Combine like terms: 0 + 6 = 6 8p + p2 = 6 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 = 6 + 16 Reorder the terms: 16 + 8p + p2 = 6 + 16 Combine like terms: 6 + 16 = 22 16 + 8p + p2 = 22 Factor a perfect square on the left side: (p + 4)(p + 4) = 22 Calculate the square root of the right side: 4.69041576 Break this problem into two subproblems by setting (p + 4) equal to 4.69041576 and -4.69041576.Subproblem 1
p + 4 = 4.69041576 Simplifying p + 4 = 4.69041576 Reorder the terms: 4 + p = 4.69041576 Solving 4 + p = 4.69041576 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 = 4.69041576 + -4 Combine like terms: 4 + -4 = 0 0 + p = 4.69041576 + -4 p = 4.69041576 + -4 Combine like terms: 4.69041576 + -4 = 0.69041576 p = 0.69041576 Simplifying p = 0.69041576Subproblem 2
p + 4 = -4.69041576 Simplifying p + 4 = -4.69041576 Reorder the terms: 4 + p = -4.69041576 Solving 4 + p = -4.69041576 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 = -4.69041576 + -4 Combine like terms: 4 + -4 = 0 0 + p = -4.69041576 + -4 p = -4.69041576 + -4 Combine like terms: -4.69041576 + -4 = -8.69041576 p = -8.69041576 Simplifying p = -8.69041576Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.69041576, -8.69041576}
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