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Simplifying 10(n2 + -12n + -90) = 0 Reorder the terms: 10(-90 + -12n + n2) = 0 (-90 * 10 + -12n * 10 + n2 * 10) = 0 (-900 + -120n + 10n2) = 0 Solving -900 + -120n + 10n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '10'. 10(-90 + -12n + n2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(-90 + -12n + n2)' equal to zero and attempt to solve: Simplifying -90 + -12n + n2 = 0 Solving -90 + -12n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '90' to each side of the equation. -90 + -12n + 90 + n2 = 0 + 90 Reorder the terms: -90 + 90 + -12n + n2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + -12n + n2 = 0 + 90 -12n + n2 = 0 + 90 Combine like terms: 0 + 90 = 90 -12n + n2 = 90 The n term is -12n. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12n + 36 + n2 = 90 + 36 Reorder the terms: 36 + -12n + n2 = 90 + 36 Combine like terms: 90 + 36 = 126 36 + -12n + n2 = 126 Factor a perfect square on the left side: (n + -6)(n + -6) = 126 Calculate the square root of the right side: 11.22497216 Break this problem into two subproblems by setting (n + -6) equal to 11.22497216 and -11.22497216.Subproblem 1
n + -6 = 11.22497216 Simplifying n + -6 = 11.22497216 Reorder the terms: -6 + n = 11.22497216 Solving -6 + n = 11.22497216 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + n = 11.22497216 + 6 Combine like terms: -6 + 6 = 0 0 + n = 11.22497216 + 6 n = 11.22497216 + 6 Combine like terms: 11.22497216 + 6 = 17.22497216 n = 17.22497216 Simplifying n = 17.22497216Subproblem 2
n + -6 = -11.22497216 Simplifying n + -6 = -11.22497216 Reorder the terms: -6 + n = -11.22497216 Solving -6 + n = -11.22497216 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + n = -11.22497216 + 6 Combine like terms: -6 + 6 = 0 0 + n = -11.22497216 + 6 n = -11.22497216 + 6 Combine like terms: -11.22497216 + 6 = -5.22497216 n = -5.22497216 Simplifying n = -5.22497216Solution
The solution to the problem is based on the solutions from the subproblems. n = {17.22497216, -5.22497216}Solution
n = {17.22497216, -5.22497216}
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