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Simplifying 20p2 + 5p + -84 = 0 Reorder the terms: -84 + 5p + 20p2 = 0 Solving -84 + 5p + 20p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -4.2 + 0.25p + p2 = 0 Move the constant term to the right: Add '4.2' to each side of the equation. -4.2 + 0.25p + 4.2 + p2 = 0 + 4.2 Reorder the terms: -4.2 + 4.2 + 0.25p + p2 = 0 + 4.2 Combine like terms: -4.2 + 4.2 = 0.0 0.0 + 0.25p + p2 = 0 + 4.2 0.25p + p2 = 0 + 4.2 Combine like terms: 0 + 4.2 = 4.2 0.25p + p2 = 4.2 The p term is 0.25p. Take half its coefficient (0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. 0.25p + 0.015625 + p2 = 4.2 + 0.015625 Reorder the terms: 0.015625 + 0.25p + p2 = 4.2 + 0.015625 Combine like terms: 4.2 + 0.015625 = 4.215625 0.015625 + 0.25p + p2 = 4.215625 Factor a perfect square on the left side: (p + 0.125)(p + 0.125) = 4.215625 Calculate the square root of the right side: 2.053198724 Break this problem into two subproblems by setting (p + 0.125) equal to 2.053198724 and -2.053198724.Subproblem 1
p + 0.125 = 2.053198724 Simplifying p + 0.125 = 2.053198724 Reorder the terms: 0.125 + p = 2.053198724 Solving 0.125 + p = 2.053198724 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + p = 2.053198724 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + p = 2.053198724 + -0.125 p = 2.053198724 + -0.125 Combine like terms: 2.053198724 + -0.125 = 1.928198724 p = 1.928198724 Simplifying p = 1.928198724Subproblem 2
p + 0.125 = -2.053198724 Simplifying p + 0.125 = -2.053198724 Reorder the terms: 0.125 + p = -2.053198724 Solving 0.125 + p = -2.053198724 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + p = -2.053198724 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + p = -2.053198724 + -0.125 p = -2.053198724 + -0.125 Combine like terms: -2.053198724 + -0.125 = -2.178198724 p = -2.178198724 Simplifying p = -2.178198724Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.928198724, -2.178198724}
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