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Simplifying -4n(7n + -5) + 8 = 168 Reorder the terms: -4n(-5 + 7n) + 8 = 168 (-5 * -4n + 7n * -4n) + 8 = 168 (20n + -28n2) + 8 = 168 Reorder the terms: 8 + 20n + -28n2 = 168 Solving 8 + 20n + -28n2 = 168 Solving for variable 'n'. Reorder the terms: 8 + -168 + 20n + -28n2 = 168 + -168 Combine like terms: 8 + -168 = -160 -160 + 20n + -28n2 = 168 + -168 Combine like terms: 168 + -168 = 0 -160 + 20n + -28n2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-40 + 5n + -7n2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-40 + 5n + -7n2)' equal to zero and attempt to solve: Simplifying -40 + 5n + -7n2 = 0 Solving -40 + 5n + -7n2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. 5.714285714 + -0.7142857143n + n2 = 0 Move the constant term to the right: Add '-5.714285714' to each side of the equation. 5.714285714 + -0.7142857143n + -5.714285714 + n2 = 0 + -5.714285714 Reorder the terms: 5.714285714 + -5.714285714 + -0.7142857143n + n2 = 0 + -5.714285714 Combine like terms: 5.714285714 + -5.714285714 = 0.000000000 0.000000000 + -0.7142857143n + n2 = 0 + -5.714285714 -0.7142857143n + n2 = 0 + -5.714285714 Combine like terms: 0 + -5.714285714 = -5.714285714 -0.7142857143n + n2 = -5.714285714 The n term is -0.7142857143n. Take half its coefficient (-0.3571428572). Square it (0.1275510204) and add it to both sides. Add '0.1275510204' to each side of the equation. -0.7142857143n + 0.1275510204 + n2 = -5.714285714 + 0.1275510204 Reorder the terms: 0.1275510204 + -0.7142857143n + n2 = -5.714285714 + 0.1275510204 Combine like terms: -5.714285714 + 0.1275510204 = -5.5867346936 0.1275510204 + -0.7142857143n + n2 = -5.5867346936 Factor a perfect square on the left side: (n + -0.3571428572)(n + -0.3571428572) = -5.5867346936 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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