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Simplifying 11p2 + -3 = 5p Reorder the terms: -3 + 11p2 = 5p Solving -3 + 11p2 = 5p Solving for variable 'p'. Reorder the terms: -3 + -5p + 11p2 = 5p + -5p Combine like terms: 5p + -5p = 0 -3 + -5p + 11p2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.2727272727 + -0.4545454545p + p2 = 0 Move the constant term to the right: Add '0.2727272727' to each side of the equation. -0.2727272727 + -0.4545454545p + 0.2727272727 + p2 = 0 + 0.2727272727 Reorder the terms: -0.2727272727 + 0.2727272727 + -0.4545454545p + p2 = 0 + 0.2727272727 Combine like terms: -0.2727272727 + 0.2727272727 = 0.0000000000 0.0000000000 + -0.4545454545p + p2 = 0 + 0.2727272727 -0.4545454545p + p2 = 0 + 0.2727272727 Combine like terms: 0 + 0.2727272727 = 0.2727272727 -0.4545454545p + p2 = 0.2727272727 The p term is -0.4545454545p. Take half its coefficient (-0.2272727273). Square it (0.05165289257) and add it to both sides. Add '0.05165289257' to each side of the equation. -0.4545454545p + 0.05165289257 + p2 = 0.2727272727 + 0.05165289257 Reorder the terms: 0.05165289257 + -0.4545454545p + p2 = 0.2727272727 + 0.05165289257 Combine like terms: 0.2727272727 + 0.05165289257 = 0.32438016527 0.05165289257 + -0.4545454545p + p2 = 0.32438016527 Factor a perfect square on the left side: (p + -0.2272727273)(p + -0.2272727273) = 0.32438016527 Calculate the square root of the right side: 0.569543822 Break this problem into two subproblems by setting (p + -0.2272727273) equal to 0.569543822 and -0.569543822.Subproblem 1
p + -0.2272727273 = 0.569543822 Simplifying p + -0.2272727273 = 0.569543822 Reorder the terms: -0.2272727273 + p = 0.569543822 Solving -0.2272727273 + p = 0.569543822 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.2272727273' to each side of the equation. -0.2272727273 + 0.2272727273 + p = 0.569543822 + 0.2272727273 Combine like terms: -0.2272727273 + 0.2272727273 = 0.0000000000 0.0000000000 + p = 0.569543822 + 0.2272727273 p = 0.569543822 + 0.2272727273 Combine like terms: 0.569543822 + 0.2272727273 = 0.7968165493 p = 0.7968165493 Simplifying p = 0.7968165493Subproblem 2
p + -0.2272727273 = -0.569543822 Simplifying p + -0.2272727273 = -0.569543822 Reorder the terms: -0.2272727273 + p = -0.569543822 Solving -0.2272727273 + p = -0.569543822 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.2272727273' to each side of the equation. -0.2272727273 + 0.2272727273 + p = -0.569543822 + 0.2272727273 Combine like terms: -0.2272727273 + 0.2272727273 = 0.0000000000 0.0000000000 + p = -0.569543822 + 0.2272727273 p = -0.569543822 + 0.2272727273 Combine like terms: -0.569543822 + 0.2272727273 = -0.3422710947 p = -0.3422710947 Simplifying p = -0.3422710947Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.7968165493, -0.3422710947}
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