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Simplifying 0.5n2 + -25n + 12 = 0 Reorder the terms: 12 + -25n + 0.5n2 = 0 Solving 12 + -25n + 0.5n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. 24 + -50n + n2 = 0 Move the constant term to the right: Add '-24' to each side of the equation. 24 + -50n + -24 + n2 = 0 + -24 Reorder the terms: 24 + -24 + -50n + n2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + -50n + n2 = 0 + -24 -50n + n2 = 0 + -24 Combine like terms: 0 + -24 = -24 -50n + n2 = -24 The n term is -50n. Take half its coefficient (-25). Square it (625) and add it to both sides. Add '625' to each side of the equation. -50n + 625 + n2 = -24 + 625 Reorder the terms: 625 + -50n + n2 = -24 + 625 Combine like terms: -24 + 625 = 601 625 + -50n + n2 = 601 Factor a perfect square on the left side: (n + -25)(n + -25) = 601 Calculate the square root of the right side: 24.515301344 Break this problem into two subproblems by setting (n + -25) equal to 24.515301344 and -24.515301344.Subproblem 1
n + -25 = 24.515301344 Simplifying n + -25 = 24.515301344 Reorder the terms: -25 + n = 24.515301344 Solving -25 + n = 24.515301344 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + n = 24.515301344 + 25 Combine like terms: -25 + 25 = 0 0 + n = 24.515301344 + 25 n = 24.515301344 + 25 Combine like terms: 24.515301344 + 25 = 49.515301344 n = 49.515301344 Simplifying n = 49.515301344Subproblem 2
n + -25 = -24.515301344 Simplifying n + -25 = -24.515301344 Reorder the terms: -25 + n = -24.515301344 Solving -25 + n = -24.515301344 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + n = -24.515301344 + 25 Combine like terms: -25 + 25 = 0 0 + n = -24.515301344 + 25 n = -24.515301344 + 25 Combine like terms: -24.515301344 + 25 = 0.484698656 n = 0.484698656 Simplifying n = 0.484698656Solution
The solution to the problem is based on the solutions from the subproblems. n = {49.515301344, 0.484698656}
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