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Simplifying 3n2 + -7n + -18 = 0 Reorder the terms: -18 + -7n + 3n2 = 0 Solving -18 + -7n + 3n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -6 + -2.333333333n + n2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -2.333333333n + 6 + n2 = 0 + 6 Reorder the terms: -6 + 6 + -2.333333333n + n2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -2.333333333n + n2 = 0 + 6 -2.333333333n + n2 = 0 + 6 Combine like terms: 0 + 6 = 6 -2.333333333n + n2 = 6 The n term is -2.333333333n. Take half its coefficient (-1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. -2.333333333n + 1.361111112 + n2 = 6 + 1.361111112 Reorder the terms: 1.361111112 + -2.333333333n + n2 = 6 + 1.361111112 Combine like terms: 6 + 1.361111112 = 7.361111112 1.361111112 + -2.333333333n + n2 = 7.361111112 Factor a perfect square on the left side: (n + -1.166666667)(n + -1.166666667) = 7.361111112 Calculate the square root of the right side: 2.713136766 Break this problem into two subproblems by setting (n + -1.166666667) equal to 2.713136766 and -2.713136766.Subproblem 1
n + -1.166666667 = 2.713136766 Simplifying n + -1.166666667 = 2.713136766 Reorder the terms: -1.166666667 + n = 2.713136766 Solving -1.166666667 + n = 2.713136766 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + n = 2.713136766 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + n = 2.713136766 + 1.166666667 n = 2.713136766 + 1.166666667 Combine like terms: 2.713136766 + 1.166666667 = 3.879803433 n = 3.879803433 Simplifying n = 3.879803433Subproblem 2
n + -1.166666667 = -2.713136766 Simplifying n + -1.166666667 = -2.713136766 Reorder the terms: -1.166666667 + n = -2.713136766 Solving -1.166666667 + n = -2.713136766 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + n = -2.713136766 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + n = -2.713136766 + 1.166666667 n = -2.713136766 + 1.166666667 Combine like terms: -2.713136766 + 1.166666667 = -1.546470099 n = -1.546470099 Simplifying n = -1.546470099Solution
The solution to the problem is based on the solutions from the subproblems. n = {3.879803433, -1.546470099}
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