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Simplifying 5n2 + -25n + -2322 = 0 Reorder the terms: -2322 + -25n + 5n2 = 0 Solving -2322 + -25n + 5n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -464.4 + -5n + n2 = 0 Move the constant term to the right: Add '464.4' to each side of the equation. -464.4 + -5n + 464.4 + n2 = 0 + 464.4 Reorder the terms: -464.4 + 464.4 + -5n + n2 = 0 + 464.4 Combine like terms: -464.4 + 464.4 = 0.0 0.0 + -5n + n2 = 0 + 464.4 -5n + n2 = 0 + 464.4 Combine like terms: 0 + 464.4 = 464.4 -5n + n2 = 464.4 The n term is -5n. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5n + 6.25 + n2 = 464.4 + 6.25 Reorder the terms: 6.25 + -5n + n2 = 464.4 + 6.25 Combine like terms: 464.4 + 6.25 = 470.65 6.25 + -5n + n2 = 470.65 Factor a perfect square on the left side: (n + -2.5)(n + -2.5) = 470.65 Calculate the square root of the right side: 21.694469341 Break this problem into two subproblems by setting (n + -2.5) equal to 21.694469341 and -21.694469341.Subproblem 1
n + -2.5 = 21.694469341 Simplifying n + -2.5 = 21.694469341 Reorder the terms: -2.5 + n = 21.694469341 Solving -2.5 + n = 21.694469341 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + n = 21.694469341 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + n = 21.694469341 + 2.5 n = 21.694469341 + 2.5 Combine like terms: 21.694469341 + 2.5 = 24.194469341 n = 24.194469341 Simplifying n = 24.194469341Subproblem 2
n + -2.5 = -21.694469341 Simplifying n + -2.5 = -21.694469341 Reorder the terms: -2.5 + n = -21.694469341 Solving -2.5 + n = -21.694469341 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + n = -21.694469341 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + n = -21.694469341 + 2.5 n = -21.694469341 + 2.5 Combine like terms: -21.694469341 + 2.5 = -19.194469341 n = -19.194469341 Simplifying n = -19.194469341Solution
The solution to the problem is based on the solutions from the subproblems. n = {24.194469341, -19.194469341}
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