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Simplifying 2n2 + -28n + 18 = 0 Reorder the terms: 18 + -28n + 2n2 = 0 Solving 18 + -28n + 2n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2'. 2(9 + -14n + n2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(9 + -14n + n2)' equal to zero and attempt to solve: Simplifying 9 + -14n + n2 = 0 Solving 9 + -14n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + -14n + -9 + n2 = 0 + -9 Reorder the terms: 9 + -9 + -14n + n2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -14n + n2 = 0 + -9 -14n + n2 = 0 + -9 Combine like terms: 0 + -9 = -9 -14n + n2 = -9 The n term is -14n. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14n + 49 + n2 = -9 + 49 Reorder the terms: 49 + -14n + n2 = -9 + 49 Combine like terms: -9 + 49 = 40 49 + -14n + n2 = 40 Factor a perfect square on the left side: (n + -7)(n + -7) = 40 Calculate the square root of the right side: 6.32455532 Break this problem into two subproblems by setting (n + -7) equal to 6.32455532 and -6.32455532.Subproblem 1
n + -7 = 6.32455532 Simplifying n + -7 = 6.32455532 Reorder the terms: -7 + n = 6.32455532 Solving -7 + n = 6.32455532 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + n = 6.32455532 + 7 Combine like terms: -7 + 7 = 0 0 + n = 6.32455532 + 7 n = 6.32455532 + 7 Combine like terms: 6.32455532 + 7 = 13.32455532 n = 13.32455532 Simplifying n = 13.32455532Subproblem 2
n + -7 = -6.32455532 Simplifying n + -7 = -6.32455532 Reorder the terms: -7 + n = -6.32455532 Solving -7 + n = -6.32455532 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + n = -6.32455532 + 7 Combine like terms: -7 + 7 = 0 0 + n = -6.32455532 + 7 n = -6.32455532 + 7 Combine like terms: -6.32455532 + 7 = 0.67544468 n = 0.67544468 Simplifying n = 0.67544468Solution
The solution to the problem is based on the solutions from the subproblems. n = {13.32455532, 0.67544468}Solution
n = {13.32455532, 0.67544468}
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