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Simplifying 8n + -40 = -4n(-5n + 1) Reorder the terms: -40 + 8n = -4n(-5n + 1) Reorder the terms: -40 + 8n = -4n(1 + -5n) -40 + 8n = (1 * -4n + -5n * -4n) -40 + 8n = (-4n + 20n2) Solving -40 + 8n = -4n + 20n2 Solving for variable 'n'. Combine like terms: 8n + 4n = 12n -40 + 12n + -20n2 = -4n + 20n2 + 4n + -20n2 Reorder the terms: -40 + 12n + -20n2 = -4n + 4n + 20n2 + -20n2 Combine like terms: -4n + 4n = 0 -40 + 12n + -20n2 = 0 + 20n2 + -20n2 -40 + 12n + -20n2 = 20n2 + -20n2 Combine like terms: 20n2 + -20n2 = 0 -40 + 12n + -20n2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-10 + 3n + -5n2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-10 + 3n + -5n2)' equal to zero and attempt to solve: Simplifying -10 + 3n + -5n2 = 0 Solving -10 + 3n + -5n2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 2 + -0.6n + n2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -0.6n + -2 + n2 = 0 + -2 Reorder the terms: 2 + -2 + -0.6n + n2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -0.6n + n2 = 0 + -2 -0.6n + n2 = 0 + -2 Combine like terms: 0 + -2 = -2 -0.6n + n2 = -2 The n term is -0.6n. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6n + 0.09 + n2 = -2 + 0.09 Reorder the terms: 0.09 + -0.6n + n2 = -2 + 0.09 Combine like terms: -2 + 0.09 = -1.91 0.09 + -0.6n + n2 = -1.91 Factor a perfect square on the left side: (n + -0.3)(n + -0.3) = -1.91 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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