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Simplifying n + -5(3n + -2) * 2n + 13 = 64 Reorder the terms: n + -5(-2 + 3n) * 2n + 13 = 64 Reorder the terms for easier multiplication: n + -5 * 2n(-2 + 3n) + 13 = 64 Multiply -5 * 2 n + -10n(-2 + 3n) + 13 = 64 n + (-2 * -10n + 3n * -10n) + 13 = 64 n + (20n + -30n2) + 13 = 64 Reorder the terms: 13 + n + 20n + -30n2 = 64 Combine like terms: n + 20n = 21n 13 + 21n + -30n2 = 64 Solving 13 + 21n + -30n2 = 64 Solving for variable 'n'. Reorder the terms: 13 + -64 + 21n + -30n2 = 64 + -64 Combine like terms: 13 + -64 = -51 -51 + 21n + -30n2 = 64 + -64 Combine like terms: 64 + -64 = 0 -51 + 21n + -30n2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-17 + 7n + -10n2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-17 + 7n + -10n2)' equal to zero and attempt to solve: Simplifying -17 + 7n + -10n2 = 0 Solving -17 + 7n + -10n2 = 0 Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. 1.7 + -0.7n + n2 = 0.0 Move the constant term to the right: Add '-1.7' to each side of the equation. 1.7 + -0.7n + -1.7 + n2 = 0.0 + -1.7 Reorder the terms: 1.7 + -1.7 + -0.7n + n2 = 0.0 + -1.7 Combine like terms: 1.7 + -1.7 = 0.0 0.0 + -0.7n + n2 = 0.0 + -1.7 -0.7n + n2 = 0.0 + -1.7 Combine like terms: 0.0 + -1.7 = -1.7 -0.7n + n2 = -1.7 The n term is -0.7n. Take half its coefficient (-0.35). Square it (0.1225) and add it to both sides. Add '0.1225' to each side of the equation. -0.7n + 0.1225 + n2 = -1.7 + 0.1225 Reorder the terms: 0.1225 + -0.7n + n2 = -1.7 + 0.1225 Combine like terms: -1.7 + 0.1225 = -1.5775 0.1225 + -0.7n + n2 = -1.5775 Factor a perfect square on the left side: (n + -0.35)(n + -0.35) = -1.5775 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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