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Simplifying 8p2 + -9 = 11p Reorder the terms: -9 + 8p2 = 11p Solving -9 + 8p2 = 11p Solving for variable 'p'. Reorder the terms: -9 + -11p + 8p2 = 11p + -11p Combine like terms: 11p + -11p = 0 -9 + -11p + 8p2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.125 + -1.375p + p2 = 0 Move the constant term to the right: Add '1.125' to each side of the equation. -1.125 + -1.375p + 1.125 + p2 = 0 + 1.125 Reorder the terms: -1.125 + 1.125 + -1.375p + p2 = 0 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + -1.375p + p2 = 0 + 1.125 -1.375p + p2 = 0 + 1.125 Combine like terms: 0 + 1.125 = 1.125 -1.375p + p2 = 1.125 The p term is -1.375p. Take half its coefficient (-0.6875). Square it (0.47265625) and add it to both sides. Add '0.47265625' to each side of the equation. -1.375p + 0.47265625 + p2 = 1.125 + 0.47265625 Reorder the terms: 0.47265625 + -1.375p + p2 = 1.125 + 0.47265625 Combine like terms: 1.125 + 0.47265625 = 1.59765625 0.47265625 + -1.375p + p2 = 1.59765625 Factor a perfect square on the left side: (p + -0.6875)(p + -0.6875) = 1.59765625 Calculate the square root of the right side: 1.263984276 Break this problem into two subproblems by setting (p + -0.6875) equal to 1.263984276 and -1.263984276.Subproblem 1
p + -0.6875 = 1.263984276 Simplifying p + -0.6875 = 1.263984276 Reorder the terms: -0.6875 + p = 1.263984276 Solving -0.6875 + p = 1.263984276 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.6875' to each side of the equation. -0.6875 + 0.6875 + p = 1.263984276 + 0.6875 Combine like terms: -0.6875 + 0.6875 = 0.0000 0.0000 + p = 1.263984276 + 0.6875 p = 1.263984276 + 0.6875 Combine like terms: 1.263984276 + 0.6875 = 1.951484276 p = 1.951484276 Simplifying p = 1.951484276Subproblem 2
p + -0.6875 = -1.263984276 Simplifying p + -0.6875 = -1.263984276 Reorder the terms: -0.6875 + p = -1.263984276 Solving -0.6875 + p = -1.263984276 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.6875' to each side of the equation. -0.6875 + 0.6875 + p = -1.263984276 + 0.6875 Combine like terms: -0.6875 + 0.6875 = 0.0000 0.0000 + p = -1.263984276 + 0.6875 p = -1.263984276 + 0.6875 Combine like terms: -1.263984276 + 0.6875 = -0.576484276 p = -0.576484276 Simplifying p = -0.576484276Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.951484276, -0.576484276}
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