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Simplifying p2 + -8p = 36 Reorder the terms: -8p + p2 = 36 Solving -8p + p2 = 36 Solving for variable 'p'. Reorder the terms: -36 + -8p + p2 = 36 + -36 Combine like terms: 36 + -36 = 0 -36 + -8p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + -8p + 36 + p2 = 0 + 36 Reorder the terms: -36 + 36 + -8p + p2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -8p + p2 = 0 + 36 -8p + p2 = 0 + 36 Combine like terms: 0 + 36 = 36 -8p + p2 = 36 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 = 36 + 16 Reorder the terms: 16 + -8p + p2 = 36 + 16 Combine like terms: 36 + 16 = 52 16 + -8p + p2 = 52 Factor a perfect square on the left side: (p + -4)(p + -4) = 52 Calculate the square root of the right side: 7.211102551 Break this problem into two subproblems by setting (p + -4) equal to 7.211102551 and -7.211102551.Subproblem 1
p + -4 = 7.211102551 Simplifying p + -4 = 7.211102551 Reorder the terms: -4 + p = 7.211102551 Solving -4 + p = 7.211102551 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 = 7.211102551 + 4 Combine like terms: -4 + 4 = 0 0 + p = 7.211102551 + 4 p = 7.211102551 + 4 Combine like terms: 7.211102551 + 4 = 11.211102551 p = 11.211102551 Simplifying p = 11.211102551Subproblem 2
p + -4 = -7.211102551 Simplifying p + -4 = -7.211102551 Reorder the terms: -4 + p = -7.211102551 Solving -4 + p = -7.211102551 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 = -7.211102551 + 4 Combine like terms: -4 + 4 = 0 0 + p = -7.211102551 + 4 p = -7.211102551 + 4 Combine like terms: -7.211102551 + 4 = -3.211102551 p = -3.211102551 Simplifying p = -3.211102551Solution
The solution to the problem is based on the solutions from the subproblems. p = {11.211102551, -3.211102551}
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