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Simplifying -12n2 + 25n + 7484 = 0 Reorder the terms: 7484 + 25n + -12n2 = 0 Solving 7484 + 25n + -12n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by -12 the coefficient of the squared term: Divide each side by '-12'. -623.6666667 + -2.083333333n + n2 = 0 Move the constant term to the right: Add '623.6666667' to each side of the equation. -623.6666667 + -2.083333333n + 623.6666667 + n2 = 0 + 623.6666667 Reorder the terms: -623.6666667 + 623.6666667 + -2.083333333n + n2 = 0 + 623.6666667 Combine like terms: -623.6666667 + 623.6666667 = 0.0000000 0.0000000 + -2.083333333n + n2 = 0 + 623.6666667 -2.083333333n + n2 = 0 + 623.6666667 Combine like terms: 0 + 623.6666667 = 623.6666667 -2.083333333n + n2 = 623.6666667 The n term is -2.083333333n. Take half its coefficient (-1.041666667). Square it (1.085069445) and add it to both sides. Add '1.085069445' to each side of the equation. -2.083333333n + 1.085069445 + n2 = 623.6666667 + 1.085069445 Reorder the terms: 1.085069445 + -2.083333333n + n2 = 623.6666667 + 1.085069445 Combine like terms: 623.6666667 + 1.085069445 = 624.751736145 1.085069445 + -2.083333333n + n2 = 624.751736145 Factor a perfect square on the left side: (n + -1.041666667)(n + -1.041666667) = 624.751736145 Calculate the square root of the right side: 24.99503423 Break this problem into two subproblems by setting (n + -1.041666667) equal to 24.99503423 and -24.99503423.Subproblem 1
n + -1.041666667 = 24.99503423 Simplifying n + -1.041666667 = 24.99503423 Reorder the terms: -1.041666667 + n = 24.99503423 Solving -1.041666667 + n = 24.99503423 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.041666667' to each side of the equation. -1.041666667 + 1.041666667 + n = 24.99503423 + 1.041666667 Combine like terms: -1.041666667 + 1.041666667 = 0.000000000 0.000000000 + n = 24.99503423 + 1.041666667 n = 24.99503423 + 1.041666667 Combine like terms: 24.99503423 + 1.041666667 = 26.036700897 n = 26.036700897 Simplifying n = 26.036700897Subproblem 2
n + -1.041666667 = -24.99503423 Simplifying n + -1.041666667 = -24.99503423 Reorder the terms: -1.041666667 + n = -24.99503423 Solving -1.041666667 + n = -24.99503423 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.041666667' to each side of the equation. -1.041666667 + 1.041666667 + n = -24.99503423 + 1.041666667 Combine like terms: -1.041666667 + 1.041666667 = 0.000000000 0.000000000 + n = -24.99503423 + 1.041666667 n = -24.99503423 + 1.041666667 Combine like terms: -24.99503423 + 1.041666667 = -23.953367563 n = -23.953367563 Simplifying n = -23.953367563Solution
The solution to the problem is based on the solutions from the subproblems. n = {26.036700897, -23.953367563}
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