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Simplifying 5n2 + -7n + -8 + -10n2 + n + 6 = 0 Reorder the terms: -8 + 6 + -7n + n + 5n2 + -10n2 = 0 Combine like terms: -8 + 6 = -2 -2 + -7n + n + 5n2 + -10n2 = 0 Combine like terms: -7n + n = -6n -2 + -6n + 5n2 + -10n2 = 0 Combine like terms: 5n2 + -10n2 = -5n2 -2 + -6n + -5n2 = 0 Solving -2 + -6n + -5n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '-1'. -1(2 + 6n + 5n2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(2 + 6n + 5n2)' equal to zero and attempt to solve: Simplifying 2 + 6n + 5n2 = 0 Solving 2 + 6n + 5n2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.4 + 1.2n + n2 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + 1.2n + -0.4 + n2 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + 1.2n + n2 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + 1.2n + n2 = 0 + -0.4 1.2n + n2 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 1.2n + n2 = -0.4 The n term is 1.2n. Take half its coefficient (0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. 1.2n + 0.36 + n2 = -0.4 + 0.36 Reorder the terms: 0.36 + 1.2n + n2 = -0.4 + 0.36 Combine like terms: -0.4 + 0.36 = -0.04 0.36 + 1.2n + n2 = -0.04 Factor a perfect square on the left side: (n + 0.6)(n + 0.6) = -0.04 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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