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Simplifying 10 + (n + -1) * 4n = 0 Reorder the terms: 10 + (-1 + n) * 4n = 0 Reorder the terms for easier multiplication: 10 + 4n(-1 + n) = 0 10 + (-1 * 4n + n * 4n) = 0 10 + (-4n + 4n2) = 0 Solving 10 + -4n + 4n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2'. 2(5 + -2n + 2n2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + -2n + 2n2)' equal to zero and attempt to solve: Simplifying 5 + -2n + 2n2 = 0 Solving 5 + -2n + 2n2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2.5 + -1n + n2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + -1n + -2.5 + n2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + -1n + n2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + -1n + n2 = 0 + -2.5 -1n + n2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 -1n + n2 = -2.5 The n term is -1n. 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 = -2.5 + 0.25 Reorder the terms: 0.25 + -1n + n2 = -2.5 + 0.25 Combine like terms: -2.5 + 0.25 = -2.25 0.25 + -1n + n2 = -2.25 Factor a perfect square on the left side: (n + -0.5)(n + -0.5) = -2.25 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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