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Simplifying p2 + -3p = 8 Reorder the terms: -3p + p2 = 8 Solving -3p + p2 = 8 Solving for variable 'p'. Reorder the terms: -8 + -3p + p2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + -3p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + -3p + 8 + p2 = 0 + 8 Reorder the terms: -8 + 8 + -3p + p2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -3p + p2 = 0 + 8 -3p + p2 = 0 + 8 Combine like terms: 0 + 8 = 8 -3p + p2 = 8 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 = 8 + 2.25 Reorder the terms: 2.25 + -3p + p2 = 8 + 2.25 Combine like terms: 8 + 2.25 = 10.25 2.25 + -3p + p2 = 10.25 Factor a perfect square on the left side: (p + -1.5)(p + -1.5) = 10.25 Calculate the square root of the right side: 3.201562119 Break this problem into two subproblems by setting (p + -1.5) equal to 3.201562119 and -3.201562119.Subproblem 1
p + -1.5 = 3.201562119 Simplifying p + -1.5 = 3.201562119 Reorder the terms: -1.5 + p = 3.201562119 Solving -1.5 + p = 3.201562119 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 = 3.201562119 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + p = 3.201562119 + 1.5 p = 3.201562119 + 1.5 Combine like terms: 3.201562119 + 1.5 = 4.701562119 p = 4.701562119 Simplifying p = 4.701562119Subproblem 2
p + -1.5 = -3.201562119 Simplifying p + -1.5 = -3.201562119 Reorder the terms: -1.5 + p = -3.201562119 Solving -1.5 + p = -3.201562119 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 = -3.201562119 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + p = -3.201562119 + 1.5 p = -3.201562119 + 1.5 Combine like terms: -3.201562119 + 1.5 = -1.701562119 p = -1.701562119 Simplifying p = -1.701562119Solution
The solution to the problem is based on the solutions from the subproblems. p = {4.701562119, -1.701562119}
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