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Simplifying 4p2 + -4p = -1p2 + 24 Reorder the terms: -4p + 4p2 = -1p2 + 24 Reorder the terms: -4p + 4p2 = 24 + -1p2 Solving -4p + 4p2 = 24 + -1p2 Solving for variable 'p'. Reorder the terms: -24 + -4p + 4p2 + p2 = 24 + -1p2 + -24 + p2 Combine like terms: 4p2 + p2 = 5p2 -24 + -4p + 5p2 = 24 + -1p2 + -24 + p2 Reorder the terms: -24 + -4p + 5p2 = 24 + -24 + -1p2 + p2 Combine like terms: 24 + -24 = 0 -24 + -4p + 5p2 = 0 + -1p2 + p2 -24 + -4p + 5p2 = -1p2 + p2 Combine like terms: -1p2 + p2 = 0 -24 + -4p + 5p2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -4.8 + -0.8p + p2 = 0 Move the constant term to the right: Add '4.8' to each side of the equation. -4.8 + -0.8p + 4.8 + p2 = 0 + 4.8 Reorder the terms: -4.8 + 4.8 + -0.8p + p2 = 0 + 4.8 Combine like terms: -4.8 + 4.8 = 0.0 0.0 + -0.8p + p2 = 0 + 4.8 -0.8p + p2 = 0 + 4.8 Combine like terms: 0 + 4.8 = 4.8 -0.8p + p2 = 4.8 The p term is -0.8p. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8p + 0.16 + p2 = 4.8 + 0.16 Reorder the terms: 0.16 + -0.8p + p2 = 4.8 + 0.16 Combine like terms: 4.8 + 0.16 = 4.96 0.16 + -0.8p + p2 = 4.96 Factor a perfect square on the left side: (p + -0.4)(p + -0.4) = 4.96 Calculate the square root of the right side: 2.227105745 Break this problem into two subproblems by setting (p + -0.4) equal to 2.227105745 and -2.227105745.Subproblem 1
p + -0.4 = 2.227105745 Simplifying p + -0.4 = 2.227105745 Reorder the terms: -0.4 + p = 2.227105745 Solving -0.4 + p = 2.227105745 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + p = 2.227105745 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + p = 2.227105745 + 0.4 p = 2.227105745 + 0.4 Combine like terms: 2.227105745 + 0.4 = 2.627105745 p = 2.627105745 Simplifying p = 2.627105745Subproblem 2
p + -0.4 = -2.227105745 Simplifying p + -0.4 = -2.227105745 Reorder the terms: -0.4 + p = -2.227105745 Solving -0.4 + p = -2.227105745 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + p = -2.227105745 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + p = -2.227105745 + 0.4 p = -2.227105745 + 0.4 Combine like terms: -2.227105745 + 0.4 = -1.827105745 p = -1.827105745 Simplifying p = -1.827105745Solution
The solution to the problem is based on the solutions from the subproblems. p = {2.627105745, -1.827105745}
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