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Simplifying 8p2 + -19p + -12 = 0 Reorder the terms: -12 + -19p + 8p2 = 0 Solving -12 + -19p + 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'. -1.5 + -2.375p + p2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -2.375p + 1.5 + p2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -2.375p + p2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -2.375p + p2 = 0 + 1.5 -2.375p + p2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -2.375p + p2 = 1.5 The p term is -2.375p. Take half its coefficient (-1.1875). Square it (1.41015625) and add it to both sides. Add '1.41015625' to each side of the equation. -2.375p + 1.41015625 + p2 = 1.5 + 1.41015625 Reorder the terms: 1.41015625 + -2.375p + p2 = 1.5 + 1.41015625 Combine like terms: 1.5 + 1.41015625 = 2.91015625 1.41015625 + -2.375p + p2 = 2.91015625 Factor a perfect square on the left side: (p + -1.1875)(p + -1.1875) = 2.91015625 Calculate the square root of the right side: 1.705918008 Break this problem into two subproblems by setting (p + -1.1875) equal to 1.705918008 and -1.705918008.Subproblem 1
p + -1.1875 = 1.705918008 Simplifying p + -1.1875 = 1.705918008 Reorder the terms: -1.1875 + p = 1.705918008 Solving -1.1875 + p = 1.705918008 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1.1875' to each side of the equation. -1.1875 + 1.1875 + p = 1.705918008 + 1.1875 Combine like terms: -1.1875 + 1.1875 = 0.0000 0.0000 + p = 1.705918008 + 1.1875 p = 1.705918008 + 1.1875 Combine like terms: 1.705918008 + 1.1875 = 2.893418008 p = 2.893418008 Simplifying p = 2.893418008Subproblem 2
p + -1.1875 = -1.705918008 Simplifying p + -1.1875 = -1.705918008 Reorder the terms: -1.1875 + p = -1.705918008 Solving -1.1875 + p = -1.705918008 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1.1875' to each side of the equation. -1.1875 + 1.1875 + p = -1.705918008 + 1.1875 Combine like terms: -1.1875 + 1.1875 = 0.0000 0.0000 + p = -1.705918008 + 1.1875 p = -1.705918008 + 1.1875 Combine like terms: -1.705918008 + 1.1875 = -0.518418008 p = -0.518418008 Simplifying p = -0.518418008Solution
The solution to the problem is based on the solutions from the subproblems. p = {2.893418008, -0.518418008}
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