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Simplifying 4p2 + -4p + -11 = 0 Reorder the terms: -11 + -4p + 4p2 = 0 Solving -11 + -4p + 4p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.75 + -1p + p2 = 0 Move the constant term to the right: Add '2.75' to each side of the equation. -2.75 + -1p + 2.75 + p2 = 0 + 2.75 Reorder the terms: -2.75 + 2.75 + -1p + p2 = 0 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + -1p + p2 = 0 + 2.75 -1p + p2 = 0 + 2.75 Combine like terms: 0 + 2.75 = 2.75 -1p + p2 = 2.75 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 = 2.75 + 0.25 Reorder the terms: 0.25 + -1p + p2 = 2.75 + 0.25 Combine like terms: 2.75 + 0.25 = 3 0.25 + -1p + p2 = 3 Factor a perfect square on the left side: (p + -0.5)(p + -0.5) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (p + -0.5) equal to 1.732050808 and -1.732050808.Subproblem 1
p + -0.5 = 1.732050808 Simplifying p + -0.5 = 1.732050808 Reorder the terms: -0.5 + p = 1.732050808 Solving -0.5 + p = 1.732050808 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 = 1.732050808 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + p = 1.732050808 + 0.5 p = 1.732050808 + 0.5 Combine like terms: 1.732050808 + 0.5 = 2.232050808 p = 2.232050808 Simplifying p = 2.232050808Subproblem 2
p + -0.5 = -1.732050808 Simplifying p + -0.5 = -1.732050808 Reorder the terms: -0.5 + p = -1.732050808 Solving -0.5 + p = -1.732050808 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 = -1.732050808 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + p = -1.732050808 + 0.5 p = -1.732050808 + 0.5 Combine like terms: -1.732050808 + 0.5 = -1.232050808 p = -1.232050808 Simplifying p = -1.232050808Solution
The solution to the problem is based on the solutions from the subproblems. p = {2.232050808, -1.232050808}
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