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Simplifying -6n2 + 25n + 35 = 0 Reorder the terms: 35 + 25n + -6n2 = 0 Solving 35 + 25n + -6n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -5.833333333 + -4.166666667n + n2 = 0 Move the constant term to the right: Add '5.833333333' to each side of the equation. -5.833333333 + -4.166666667n + 5.833333333 + n2 = 0 + 5.833333333 Reorder the terms: -5.833333333 + 5.833333333 + -4.166666667n + n2 = 0 + 5.833333333 Combine like terms: -5.833333333 + 5.833333333 = 0.000000000 0.000000000 + -4.166666667n + n2 = 0 + 5.833333333 -4.166666667n + n2 = 0 + 5.833333333 Combine like terms: 0 + 5.833333333 = 5.833333333 -4.166666667n + n2 = 5.833333333 The n term is -4.166666667n. Take half its coefficient (-2.083333334). Square it (4.340277781) and add it to both sides. Add '4.340277781' to each side of the equation. -4.166666667n + 4.340277781 + n2 = 5.833333333 + 4.340277781 Reorder the terms: 4.340277781 + -4.166666667n + n2 = 5.833333333 + 4.340277781 Combine like terms: 5.833333333 + 4.340277781 = 10.173611114 4.340277781 + -4.166666667n + n2 = 10.173611114 Factor a perfect square on the left side: (n + -2.083333334)(n + -2.083333334) = 10.173611114 Calculate the square root of the right side: 3.189609869 Break this problem into two subproblems by setting (n + -2.083333334) equal to 3.189609869 and -3.189609869.Subproblem 1
n + -2.083333334 = 3.189609869 Simplifying n + -2.083333334 = 3.189609869 Reorder the terms: -2.083333334 + n = 3.189609869 Solving -2.083333334 + n = 3.189609869 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2.083333334' to each side of the equation. -2.083333334 + 2.083333334 + n = 3.189609869 + 2.083333334 Combine like terms: -2.083333334 + 2.083333334 = 0.000000000 0.000000000 + n = 3.189609869 + 2.083333334 n = 3.189609869 + 2.083333334 Combine like terms: 3.189609869 + 2.083333334 = 5.272943203 n = 5.272943203 Simplifying n = 5.272943203Subproblem 2
n + -2.083333334 = -3.189609869 Simplifying n + -2.083333334 = -3.189609869 Reorder the terms: -2.083333334 + n = -3.189609869 Solving -2.083333334 + n = -3.189609869 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2.083333334' to each side of the equation. -2.083333334 + 2.083333334 + n = -3.189609869 + 2.083333334 Combine like terms: -2.083333334 + 2.083333334 = 0.000000000 0.000000000 + n = -3.189609869 + 2.083333334 n = -3.189609869 + 2.083333334 Combine like terms: -3.189609869 + 2.083333334 = -1.106276535 n = -1.106276535 Simplifying n = -1.106276535Solution
The solution to the problem is based on the solutions from the subproblems. n = {5.272943203, -1.106276535}
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