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Simplifying 2 + 9p + -2p2 = 4 Solving 2 + 9p + -2p2 = 4 Solving for variable 'p'. Reorder the terms: 2 + -4 + 9p + -2p2 = 4 + -4 Combine like terms: 2 + -4 = -2 -2 + 9p + -2p2 = 4 + -4 Combine like terms: 4 + -4 = 0 -2 + 9p + -2p2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 1 + -4.5p + p2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -4.5p + -1 + p2 = 0 + -1 Reorder the terms: 1 + -1 + -4.5p + p2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4.5p + p2 = 0 + -1 -4.5p + p2 = 0 + -1 Combine like terms: 0 + -1 = -1 -4.5p + p2 = -1 The p term is -4.5p. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5p + 5.0625 + p2 = -1 + 5.0625 Reorder the terms: 5.0625 + -4.5p + p2 = -1 + 5.0625 Combine like terms: -1 + 5.0625 = 4.0625 5.0625 + -4.5p + p2 = 4.0625 Factor a perfect square on the left side: (p + -2.25)(p + -2.25) = 4.0625 Calculate the square root of the right side: 2.015564437 Break this problem into two subproblems by setting (p + -2.25) equal to 2.015564437 and -2.015564437.Subproblem 1
p + -2.25 = 2.015564437 Simplifying p + -2.25 = 2.015564437 Reorder the terms: -2.25 + p = 2.015564437 Solving -2.25 + p = 2.015564437 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + p = 2.015564437 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + p = 2.015564437 + 2.25 p = 2.015564437 + 2.25 Combine like terms: 2.015564437 + 2.25 = 4.265564437 p = 4.265564437 Simplifying p = 4.265564437Subproblem 2
p + -2.25 = -2.015564437 Simplifying p + -2.25 = -2.015564437 Reorder the terms: -2.25 + p = -2.015564437 Solving -2.25 + p = -2.015564437 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + p = -2.015564437 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + p = -2.015564437 + 2.25 p = -2.015564437 + 2.25 Combine like terms: -2.015564437 + 2.25 = 0.234435563 p = 0.234435563 Simplifying p = 0.234435563Solution
The solution to the problem is based on the solutions from the subproblems. p = {4.265564437, 0.234435563}
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