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Simplifying p2 + -3p + -24 = 0 Reorder the terms: -24 + -3p + p2 = 0 Solving -24 + -3p + p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '24' to each side of the equation. -24 + -3p + 24 + p2 = 0 + 24 Reorder the terms: -24 + 24 + -3p + p2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -3p + p2 = 0 + 24 -3p + p2 = 0 + 24 Combine like terms: 0 + 24 = 24 -3p + p2 = 24 The p term is -3p. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3p + 2.25 + p2 = 24 + 2.25 Reorder the terms: 2.25 + -3p + p2 = 24 + 2.25 Combine like terms: 24 + 2.25 = 26.25 2.25 + -3p + p2 = 26.25 Factor a perfect square on the left side: (p + -1.5)(p + -1.5) = 26.25 Calculate the square root of the right side: 5.123475383 Break this problem into two subproblems by setting (p + -1.5) equal to 5.123475383 and -5.123475383.Subproblem 1
p + -1.5 = 5.123475383 Simplifying p + -1.5 = 5.123475383 Reorder the terms: -1.5 + p = 5.123475383 Solving -1.5 + p = 5.123475383 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + p = 5.123475383 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + p = 5.123475383 + 1.5 p = 5.123475383 + 1.5 Combine like terms: 5.123475383 + 1.5 = 6.623475383 p = 6.623475383 Simplifying p = 6.623475383Subproblem 2
p + -1.5 = -5.123475383 Simplifying p + -1.5 = -5.123475383 Reorder the terms: -1.5 + p = -5.123475383 Solving -1.5 + p = -5.123475383 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + p = -5.123475383 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + p = -5.123475383 + 1.5 p = -5.123475383 + 1.5 Combine like terms: -5.123475383 + 1.5 = -3.623475383 p = -3.623475383 Simplifying p = -3.623475383Solution
The solution to the problem is based on the solutions from the subproblems. p = {6.623475383, -3.623475383}
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