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Simplifying 7n5(8n2 + -8n + 4) = 0 Reorder the terms: 7n5(4 + -8n + 8n2) = 0 (4 * 7n5 + -8n * 7n5 + 8n2 * 7n5) = 0 (28n5 + -56n6 + 56n7) = 0 Solving 28n5 + -56n6 + 56n7 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '28n5'. 28n5(1 + -2n + 2n2) = 0 Ignore the factor 28.Subproblem 1
Set the factor 'n5' equal to zero and attempt to solve: Simplifying n5 = 0 Solving n5 = 0 Move all terms containing n to the left, all other terms to the right. Simplifying n5 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(1 + -2n + 2n2)' equal to zero and attempt to solve: Simplifying 1 + -2n + 2n2 = 0 Solving 1 + -2n + 2n2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 0.5 + -1n + n2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -1n + -0.5 + n2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -1n + n2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -1n + n2 = 0 + -0.5 -1n + n2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -1n + n2 = -0.5 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 = -0.5 + 0.25 Reorder the terms: 0.25 + -1n + n2 = -0.5 + 0.25 Combine like terms: -0.5 + 0.25 = -0.25 0.25 + -1n + n2 = -0.25 Factor a perfect square on the left side: (n + -0.5)(n + -0.5) = -0.25 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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