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Simplifying 0 = p2 + -9p + -4 Reorder the terms: 0 = -4 + -9p + p2 Solving 0 = -4 + -9p + p2 Solving for variable 'p'. Combine like terms: 0 + 4 = 4 4 + 9p + -1p2 = -4 + -9p + p2 + 4 + 9p + -1p2 Reorder the terms: 4 + 9p + -1p2 = -4 + 4 + -9p + 9p + p2 + -1p2 Combine like terms: -4 + 4 = 0 4 + 9p + -1p2 = 0 + -9p + 9p + p2 + -1p2 4 + 9p + -1p2 = -9p + 9p + p2 + -1p2 Combine like terms: -9p + 9p = 0 4 + 9p + -1p2 = 0 + p2 + -1p2 4 + 9p + -1p2 = p2 + -1p2 Combine like terms: p2 + -1p2 = 0 4 + 9p + -1p2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -4 + -9p + p2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -9p + 4 + p2 = 0 + 4 Reorder the terms: -4 + 4 + -9p + p2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -9p + p2 = 0 + 4 -9p + p2 = 0 + 4 Combine like terms: 0 + 4 = 4 -9p + p2 = 4 The p term is -9p. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9p + 20.25 + p2 = 4 + 20.25 Reorder the terms: 20.25 + -9p + p2 = 4 + 20.25 Combine like terms: 4 + 20.25 = 24.25 20.25 + -9p + p2 = 24.25 Factor a perfect square on the left side: (p + -4.5)(p + -4.5) = 24.25 Calculate the square root of the right side: 4.924428901 Break this problem into two subproblems by setting (p + -4.5) equal to 4.924428901 and -4.924428901.Subproblem 1
p + -4.5 = 4.924428901 Simplifying p + -4.5 = 4.924428901 Reorder the terms: -4.5 + p = 4.924428901 Solving -4.5 + p = 4.924428901 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + p = 4.924428901 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + p = 4.924428901 + 4.5 p = 4.924428901 + 4.5 Combine like terms: 4.924428901 + 4.5 = 9.424428901 p = 9.424428901 Simplifying p = 9.424428901Subproblem 2
p + -4.5 = -4.924428901 Simplifying p + -4.5 = -4.924428901 Reorder the terms: -4.5 + p = -4.924428901 Solving -4.5 + p = -4.924428901 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + p = -4.924428901 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + p = -4.924428901 + 4.5 p = -4.924428901 + 4.5 Combine like terms: -4.924428901 + 4.5 = -0.424428901 p = -0.424428901 Simplifying p = -0.424428901Solution
The solution to the problem is based on the solutions from the subproblems. p = {9.424428901, -0.424428901}
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