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Simplifying (-8p2 + -9p + 9) + (6p + -8) = 0 Reorder the terms: (9 + -9p + -8p2) + (6p + -8) = 0 Remove parenthesis around (9 + -9p + -8p2) 9 + -9p + -8p2 + (6p + -8) = 0 Reorder the terms: 9 + -9p + -8p2 + (-8 + 6p) = 0 Remove parenthesis around (-8 + 6p) 9 + -9p + -8p2 + -8 + 6p = 0 Reorder the terms: 9 + -8 + -9p + 6p + -8p2 = 0 Combine like terms: 9 + -8 = 1 1 + -9p + 6p + -8p2 = 0 Combine like terms: -9p + 6p = -3p 1 + -3p + -8p2 = 0 Solving 1 + -3p + -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'. -0.125 + 0.375p + p2 = 0 Move the constant term to the right: Add '0.125' to each side of the equation. -0.125 + 0.375p + 0.125 + p2 = 0 + 0.125 Reorder the terms: -0.125 + 0.125 + 0.375p + p2 = 0 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + 0.375p + p2 = 0 + 0.125 0.375p + p2 = 0 + 0.125 Combine like terms: 0 + 0.125 = 0.125 0.375p + p2 = 0.125 The p term is 0.375p. Take half its coefficient (0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. 0.375p + 0.03515625 + p2 = 0.125 + 0.03515625 Reorder the terms: 0.03515625 + 0.375p + p2 = 0.125 + 0.03515625 Combine like terms: 0.125 + 0.03515625 = 0.16015625 0.03515625 + 0.375p + p2 = 0.16015625 Factor a perfect square on the left side: (p + 0.1875)(p + 0.1875) = 0.16015625 Calculate the square root of the right side: 0.400195265 Break this problem into two subproblems by setting (p + 0.1875) equal to 0.400195265 and -0.400195265.Subproblem 1
p + 0.1875 = 0.400195265 Simplifying p + 0.1875 = 0.400195265 Reorder the terms: 0.1875 + p = 0.400195265 Solving 0.1875 + p = 0.400195265 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.1875' to each side of the equation. 0.1875 + -0.1875 + p = 0.400195265 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + p = 0.400195265 + -0.1875 p = 0.400195265 + -0.1875 Combine like terms: 0.400195265 + -0.1875 = 0.212695265 p = 0.212695265 Simplifying p = 0.212695265Subproblem 2
p + 0.1875 = -0.400195265 Simplifying p + 0.1875 = -0.400195265 Reorder the terms: 0.1875 + p = -0.400195265 Solving 0.1875 + p = -0.400195265 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.1875' to each side of the equation. 0.1875 + -0.1875 + p = -0.400195265 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + p = -0.400195265 + -0.1875 p = -0.400195265 + -0.1875 Combine like terms: -0.400195265 + -0.1875 = -0.587695265 p = -0.587695265 Simplifying p = -0.587695265Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.212695265, -0.587695265}
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