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Simplifying 8n(3n + 5) = -32 Reorder the terms: 8n(5 + 3n) = -32 (5 * 8n + 3n * 8n) = -32 (40n + 24n2) = -32 Solving 40n + 24n2 = -32 Solving for variable 'n'. Reorder the terms: 32 + 40n + 24n2 = -32 + 32 Combine like terms: -32 + 32 = 0 32 + 40n + 24n2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(4 + 5n + 3n2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(4 + 5n + 3n2)' equal to zero and attempt to solve: Simplifying 4 + 5n + 3n2 = 0 Solving 4 + 5n + 3n2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1.333333333 + 1.666666667n + n2 = 0 Move the constant term to the right: Add '-1.333333333' to each side of the equation. 1.333333333 + 1.666666667n + -1.333333333 + n2 = 0 + -1.333333333 Reorder the terms: 1.333333333 + -1.333333333 + 1.666666667n + n2 = 0 + -1.333333333 Combine like terms: 1.333333333 + -1.333333333 = 0.000000000 0.000000000 + 1.666666667n + n2 = 0 + -1.333333333 1.666666667n + n2 = 0 + -1.333333333 Combine like terms: 0 + -1.333333333 = -1.333333333 1.666666667n + n2 = -1.333333333 The n term is 1.666666667n. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667n + 0.6944444447 + n2 = -1.333333333 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667n + n2 = -1.333333333 + 0.6944444447 Combine like terms: -1.333333333 + 0.6944444447 = -0.6388888883 0.6944444447 + 1.666666667n + n2 = -0.6388888883 Factor a perfect square on the left side: (n + 0.8333333335)(n + 0.8333333335) = -0.6388888883 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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