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Simplifying -37 + -7n = 7n(5n + -7) + -2 Reorder the terms: -37 + -7n = 7n(-7 + 5n) + -2 -37 + -7n = (-7 * 7n + 5n * 7n) + -2 -37 + -7n = (-49n + 35n2) + -2 Reorder the terms: -37 + -7n = -2 + -49n + 35n2 Solving -37 + -7n = -2 + -49n + 35n2 Solving for variable 'n'. Reorder the terms: -37 + 2 + -7n + 49n + -35n2 = -2 + -49n + 35n2 + 2 + 49n + -35n2 Combine like terms: -37 + 2 = -35 -35 + -7n + 49n + -35n2 = -2 + -49n + 35n2 + 2 + 49n + -35n2 Combine like terms: -7n + 49n = 42n -35 + 42n + -35n2 = -2 + -49n + 35n2 + 2 + 49n + -35n2 Reorder the terms: -35 + 42n + -35n2 = -2 + 2 + -49n + 49n + 35n2 + -35n2 Combine like terms: -2 + 2 = 0 -35 + 42n + -35n2 = 0 + -49n + 49n + 35n2 + -35n2 -35 + 42n + -35n2 = -49n + 49n + 35n2 + -35n2 Combine like terms: -49n + 49n = 0 -35 + 42n + -35n2 = 0 + 35n2 + -35n2 -35 + 42n + -35n2 = 35n2 + -35n2 Combine like terms: 35n2 + -35n2 = 0 -35 + 42n + -35n2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(-5 + 6n + -5n2) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(-5 + 6n + -5n2)' equal to zero and attempt to solve: Simplifying -5 + 6n + -5n2 = 0 Solving -5 + 6n + -5n2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 1 + -1.2n + n2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -1.2n + -1 + n2 = 0 + -1 Reorder the terms: 1 + -1 + -1.2n + n2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1.2n + n2 = 0 + -1 -1.2n + n2 = 0 + -1 Combine like terms: 0 + -1 = -1 -1.2n + n2 = -1 The n term is -1.2n. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2n + 0.36 + n2 = -1 + 0.36 Reorder the terms: 0.36 + -1.2n + n2 = -1 + 0.36 Combine like terms: -1 + 0.36 = -0.64 0.36 + -1.2n + n2 = -0.64 Factor a perfect square on the left side: (n + -0.6)(n + -0.6) = -0.64 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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