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Simplifying 4n2 + 38n + 540 = 0 Reorder the terms: 540 + 38n + 4n2 = 0 Solving 540 + 38n + 4n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2'. 2(270 + 19n + 2n2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(270 + 19n + 2n2)' equal to zero and attempt to solve: Simplifying 270 + 19n + 2n2 = 0 Solving 270 + 19n + 2n2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 135 + 9.5n + n2 = 0 Move the constant term to the right: Add '-135' to each side of the equation. 135 + 9.5n + -135 + n2 = 0 + -135 Reorder the terms: 135 + -135 + 9.5n + n2 = 0 + -135 Combine like terms: 135 + -135 = 0 0 + 9.5n + n2 = 0 + -135 9.5n + n2 = 0 + -135 Combine like terms: 0 + -135 = -135 9.5n + n2 = -135 The n term is 9.5n. Take half its coefficient (4.75). Square it (22.5625) and add it to both sides. Add '22.5625' to each side of the equation. 9.5n + 22.5625 + n2 = -135 + 22.5625 Reorder the terms: 22.5625 + 9.5n + n2 = -135 + 22.5625 Combine like terms: -135 + 22.5625 = -112.4375 22.5625 + 9.5n + n2 = -112.4375 Factor a perfect square on the left side: (n + 4.75)(n + 4.75) = -112.4375 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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