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Simplifying 4p2 + -19p = -2 Reorder the terms: -19p + 4p2 = -2 Solving -19p + 4p2 = -2 Solving for variable 'p'. Reorder the terms: 2 + -19p + 4p2 = -2 + 2 Combine like terms: -2 + 2 = 0 2 + -19p + 4p2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.5 + -4.75p + p2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -4.75p + -0.5 + p2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -4.75p + p2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -4.75p + p2 = 0 + -0.5 -4.75p + p2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -4.75p + p2 = -0.5 The p term is -4.75p. Take half its coefficient (-2.375). Square it (5.640625) and add it to both sides. Add '5.640625' to each side of the equation. -4.75p + 5.640625 + p2 = -0.5 + 5.640625 Reorder the terms: 5.640625 + -4.75p + p2 = -0.5 + 5.640625 Combine like terms: -0.5 + 5.640625 = 5.140625 5.640625 + -4.75p + p2 = 5.140625 Factor a perfect square on the left side: (p + -2.375)(p + -2.375) = 5.140625 Calculate the square root of the right side: 2.267294643 Break this problem into two subproblems by setting (p + -2.375) equal to 2.267294643 and -2.267294643.Subproblem 1
p + -2.375 = 2.267294643 Simplifying p + -2.375 = 2.267294643 Reorder the terms: -2.375 + p = 2.267294643 Solving -2.375 + p = 2.267294643 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '2.375' to each side of the equation. -2.375 + 2.375 + p = 2.267294643 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + p = 2.267294643 + 2.375 p = 2.267294643 + 2.375 Combine like terms: 2.267294643 + 2.375 = 4.642294643 p = 4.642294643 Simplifying p = 4.642294643Subproblem 2
p + -2.375 = -2.267294643 Simplifying p + -2.375 = -2.267294643 Reorder the terms: -2.375 + p = -2.267294643 Solving -2.375 + p = -2.267294643 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '2.375' to each side of the equation. -2.375 + 2.375 + p = -2.267294643 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + p = -2.267294643 + 2.375 p = -2.267294643 + 2.375 Combine like terms: -2.267294643 + 2.375 = 0.107705357 p = 0.107705357 Simplifying p = 0.107705357Solution
The solution to the problem is based on the solutions from the subproblems. p = {4.642294643, 0.107705357}
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