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Simplifying 49p2 + -28p + -2 = 0 Reorder the terms: -2 + -28p + 49p2 = 0 Solving -2 + -28p + 49p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. -0.04081632653 + -0.5714285714p + p2 = 0 Move the constant term to the right: Add '0.04081632653' to each side of the equation. -0.04081632653 + -0.5714285714p + 0.04081632653 + p2 = 0 + 0.04081632653 Reorder the terms: -0.04081632653 + 0.04081632653 + -0.5714285714p + p2 = 0 + 0.04081632653 Combine like terms: -0.04081632653 + 0.04081632653 = 0.00000000000 0.00000000000 + -0.5714285714p + p2 = 0 + 0.04081632653 -0.5714285714p + p2 = 0 + 0.04081632653 Combine like terms: 0 + 0.04081632653 = 0.04081632653 -0.5714285714p + p2 = 0.04081632653 The p term is -0.5714285714p. Take half its coefficient (-0.2857142857). Square it (0.08163265305) and add it to both sides. Add '0.08163265305' to each side of the equation. -0.5714285714p + 0.08163265305 + p2 = 0.04081632653 + 0.08163265305 Reorder the terms: 0.08163265305 + -0.5714285714p + p2 = 0.04081632653 + 0.08163265305 Combine like terms: 0.04081632653 + 0.08163265305 = 0.12244897958 0.08163265305 + -0.5714285714p + p2 = 0.12244897958 Factor a perfect square on the left side: (p + -0.2857142857)(p + -0.2857142857) = 0.12244897958 Calculate the square root of the right side: 0.349927106 Break this problem into two subproblems by setting (p + -0.2857142857) equal to 0.349927106 and -0.349927106.Subproblem 1
p + -0.2857142857 = 0.349927106 Simplifying p + -0.2857142857 = 0.349927106 Reorder the terms: -0.2857142857 + p = 0.349927106 Solving -0.2857142857 + p = 0.349927106 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + p = 0.349927106 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + p = 0.349927106 + 0.2857142857 p = 0.349927106 + 0.2857142857 Combine like terms: 0.349927106 + 0.2857142857 = 0.6356413917 p = 0.6356413917 Simplifying p = 0.6356413917Subproblem 2
p + -0.2857142857 = -0.349927106 Simplifying p + -0.2857142857 = -0.349927106 Reorder the terms: -0.2857142857 + p = -0.349927106 Solving -0.2857142857 + p = -0.349927106 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + p = -0.349927106 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + p = -0.349927106 + 0.2857142857 p = -0.349927106 + 0.2857142857 Combine like terms: -0.349927106 + 0.2857142857 = -0.0642128203 p = -0.0642128203 Simplifying p = -0.0642128203Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.6356413917, -0.0642128203}
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