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Simplifying 2p2 + -20p + 13 = 0 Reorder the terms: 13 + -20p + 2p2 = 0 Solving 13 + -20p + 2p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 6.5 + -10p + p2 = 0 Move the constant term to the right: Add '-6.5' to each side of the equation. 6.5 + -10p + -6.5 + p2 = 0 + -6.5 Reorder the terms: 6.5 + -6.5 + -10p + p2 = 0 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + -10p + p2 = 0 + -6.5 -10p + p2 = 0 + -6.5 Combine like terms: 0 + -6.5 = -6.5 -10p + p2 = -6.5 The p term is -10p. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10p + 25 + p2 = -6.5 + 25 Reorder the terms: 25 + -10p + p2 = -6.5 + 25 Combine like terms: -6.5 + 25 = 18.5 25 + -10p + p2 = 18.5 Factor a perfect square on the left side: (p + -5)(p + -5) = 18.5 Calculate the square root of the right side: 4.301162634 Break this problem into two subproblems by setting (p + -5) equal to 4.301162634 and -4.301162634.Subproblem 1
p + -5 = 4.301162634 Simplifying p + -5 = 4.301162634 Reorder the terms: -5 + p = 4.301162634 Solving -5 + p = 4.301162634 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + p = 4.301162634 + 5 Combine like terms: -5 + 5 = 0 0 + p = 4.301162634 + 5 p = 4.301162634 + 5 Combine like terms: 4.301162634 + 5 = 9.301162634 p = 9.301162634 Simplifying p = 9.301162634Subproblem 2
p + -5 = -4.301162634 Simplifying p + -5 = -4.301162634 Reorder the terms: -5 + p = -4.301162634 Solving -5 + p = -4.301162634 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + p = -4.301162634 + 5 Combine like terms: -5 + 5 = 0 0 + p = -4.301162634 + 5 p = -4.301162634 + 5 Combine like terms: -4.301162634 + 5 = 0.698837366 p = 0.698837366 Simplifying p = 0.698837366Solution
The solution to the problem is based on the solutions from the subproblems. p = {9.301162634, 0.698837366}
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