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Simplifying 9p2 + -7 = 9p Reorder the terms: -7 + 9p2 = 9p Solving -7 + 9p2 = 9p Solving for variable 'p'. Reorder the terms: -7 + -9p + 9p2 = 9p + -9p Combine like terms: 9p + -9p = 0 -7 + -9p + 9p2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.7777777778 + -1p + p2 = 0 Move the constant term to the right: Add '0.7777777778' to each side of the equation. -0.7777777778 + -1p + 0.7777777778 + p2 = 0 + 0.7777777778 Reorder the terms: -0.7777777778 + 0.7777777778 + -1p + p2 = 0 + 0.7777777778 Combine like terms: -0.7777777778 + 0.7777777778 = 0.0000000000 0.0000000000 + -1p + p2 = 0 + 0.7777777778 -1p + p2 = 0 + 0.7777777778 Combine like terms: 0 + 0.7777777778 = 0.7777777778 -1p + p2 = 0.7777777778 The p term is -1p. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1p + 0.25 + p2 = 0.7777777778 + 0.25 Reorder the terms: 0.25 + -1p + p2 = 0.7777777778 + 0.25 Combine like terms: 0.7777777778 + 0.25 = 1.0277777778 0.25 + -1p + p2 = 1.0277777778 Factor a perfect square on the left side: (p + -0.5)(p + -0.5) = 1.0277777778 Calculate the square root of the right side: 1.013793755 Break this problem into two subproblems by setting (p + -0.5) equal to 1.013793755 and -1.013793755.Subproblem 1
p + -0.5 = 1.013793755 Simplifying p + -0.5 = 1.013793755 Reorder the terms: -0.5 + p = 1.013793755 Solving -0.5 + p = 1.013793755 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + p = 1.013793755 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + p = 1.013793755 + 0.5 p = 1.013793755 + 0.5 Combine like terms: 1.013793755 + 0.5 = 1.513793755 p = 1.513793755 Simplifying p = 1.513793755Subproblem 2
p + -0.5 = -1.013793755 Simplifying p + -0.5 = -1.013793755 Reorder the terms: -0.5 + p = -1.013793755 Solving -0.5 + p = -1.013793755 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + p = -1.013793755 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + p = -1.013793755 + 0.5 p = -1.013793755 + 0.5 Combine like terms: -1.013793755 + 0.5 = -0.513793755 p = -0.513793755 Simplifying p = -0.513793755Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.513793755, -0.513793755}
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