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Simplifying 8p2 + -21p + -36 = 0 Reorder the terms: -36 + -21p + 8p2 = 0 Solving -36 + -21p + 8p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -4.5 + -2.625p + p2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + -2.625p + 4.5 + p2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + -2.625p + p2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + -2.625p + p2 = 0 + 4.5 -2.625p + p2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 -2.625p + p2 = 4.5 The p term is -2.625p. Take half its coefficient (-1.3125). Square it (1.72265625) and add it to both sides. Add '1.72265625' to each side of the equation. -2.625p + 1.72265625 + p2 = 4.5 + 1.72265625 Reorder the terms: 1.72265625 + -2.625p + p2 = 4.5 + 1.72265625 Combine like terms: 4.5 + 1.72265625 = 6.22265625 1.72265625 + -2.625p + p2 = 6.22265625 Factor a perfect square on the left side: (p + -1.3125)(p + -1.3125) = 6.22265625 Calculate the square root of the right side: 2.494525255 Break this problem into two subproblems by setting (p + -1.3125) equal to 2.494525255 and -2.494525255.Subproblem 1
p + -1.3125 = 2.494525255 Simplifying p + -1.3125 = 2.494525255 Reorder the terms: -1.3125 + p = 2.494525255 Solving -1.3125 + p = 2.494525255 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1.3125' to each side of the equation. -1.3125 + 1.3125 + p = 2.494525255 + 1.3125 Combine like terms: -1.3125 + 1.3125 = 0.0000 0.0000 + p = 2.494525255 + 1.3125 p = 2.494525255 + 1.3125 Combine like terms: 2.494525255 + 1.3125 = 3.807025255 p = 3.807025255 Simplifying p = 3.807025255Subproblem 2
p + -1.3125 = -2.494525255 Simplifying p + -1.3125 = -2.494525255 Reorder the terms: -1.3125 + p = -2.494525255 Solving -1.3125 + p = -2.494525255 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1.3125' to each side of the equation. -1.3125 + 1.3125 + p = -2.494525255 + 1.3125 Combine like terms: -1.3125 + 1.3125 = 0.0000 0.0000 + p = -2.494525255 + 1.3125 p = -2.494525255 + 1.3125 Combine like terms: -2.494525255 + 1.3125 = -1.182025255 p = -1.182025255 Simplifying p = -1.182025255Solution
The solution to the problem is based on the solutions from the subproblems. p = {3.807025255, -1.182025255}
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