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Simplifying 9p2 + 5p + -5 = 0 Reorder the terms: -5 + 5p + 9p2 = 0 Solving -5 + 5p + 9p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.5555555556 + 0.5555555556p + p2 = 0 Move the constant term to the right: Add '0.5555555556' to each side of the equation. -0.5555555556 + 0.5555555556p + 0.5555555556 + p2 = 0 + 0.5555555556 Reorder the terms: -0.5555555556 + 0.5555555556 + 0.5555555556p + p2 = 0 + 0.5555555556 Combine like terms: -0.5555555556 + 0.5555555556 = 0.0000000000 0.0000000000 + 0.5555555556p + p2 = 0 + 0.5555555556 0.5555555556p + p2 = 0 + 0.5555555556 Combine like terms: 0 + 0.5555555556 = 0.5555555556 0.5555555556p + p2 = 0.5555555556 The p term is 0.5555555556p. Take half its coefficient (0.2777777778). Square it (0.07716049384) and add it to both sides. Add '0.07716049384' to each side of the equation. 0.5555555556p + 0.07716049384 + p2 = 0.5555555556 + 0.07716049384 Reorder the terms: 0.07716049384 + 0.5555555556p + p2 = 0.5555555556 + 0.07716049384 Combine like terms: 0.5555555556 + 0.07716049384 = 0.63271604944 0.07716049384 + 0.5555555556p + p2 = 0.63271604944 Factor a perfect square on the left side: (p + 0.2777777778)(p + 0.2777777778) = 0.63271604944 Calculate the square root of the right side: 0.795434504 Break this problem into two subproblems by setting (p + 0.2777777778) equal to 0.795434504 and -0.795434504.Subproblem 1
p + 0.2777777778 = 0.795434504 Simplifying p + 0.2777777778 = 0.795434504 Reorder the terms: 0.2777777778 + p = 0.795434504 Solving 0.2777777778 + p = 0.795434504 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.2777777778' to each side of the equation. 0.2777777778 + -0.2777777778 + p = 0.795434504 + -0.2777777778 Combine like terms: 0.2777777778 + -0.2777777778 = 0.0000000000 0.0000000000 + p = 0.795434504 + -0.2777777778 p = 0.795434504 + -0.2777777778 Combine like terms: 0.795434504 + -0.2777777778 = 0.5176567262 p = 0.5176567262 Simplifying p = 0.5176567262Subproblem 2
p + 0.2777777778 = -0.795434504 Simplifying p + 0.2777777778 = -0.795434504 Reorder the terms: 0.2777777778 + p = -0.795434504 Solving 0.2777777778 + p = -0.795434504 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.2777777778' to each side of the equation. 0.2777777778 + -0.2777777778 + p = -0.795434504 + -0.2777777778 Combine like terms: 0.2777777778 + -0.2777777778 = 0.0000000000 0.0000000000 + p = -0.795434504 + -0.2777777778 p = -0.795434504 + -0.2777777778 Combine like terms: -0.795434504 + -0.2777777778 = -1.0732122818 p = -1.0732122818 Simplifying p = -1.0732122818Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.5176567262, -1.0732122818}
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