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Simplifying 7(1 + -1n) * n = 63 Reorder the terms for easier multiplication: 7n(1 + -1n) = 63 (1 * 7n + -1n * 7n) = 63 (7n + -7n2) = 63 Solving 7n + -7n2 = 63 Solving for variable 'n'. Reorder the terms: -63 + 7n + -7n2 = 63 + -63 Combine like terms: 63 + -63 = 0 -63 + 7n + -7n2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(-9 + n + -1n2) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(-9 + n + -1n2)' equal to zero and attempt to solve: Simplifying -9 + n + -1n2 = 0 Solving -9 + n + -1n2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 9 + -1n + n2 = 0 Move the constant term to the right: Add '-9' to each side of the equation. 9 + -1n + -9 + n2 = 0 + -9 Reorder the terms: 9 + -9 + -1n + n2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1n + n2 = 0 + -9 -1n + n2 = 0 + -9 Combine like terms: 0 + -9 = -9 -1n + n2 = -9 The n term is n. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1n + 0.25 + n2 = -9 + 0.25 Reorder the terms: 0.25 + -1n + n2 = -9 + 0.25 Combine like terms: -9 + 0.25 = -8.75 0.25 + -1n + n2 = -8.75 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = -8.75 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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