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Simplifying -3n(n + 4) = 21 Reorder the terms: -3n(4 + n) = 21 (4 * -3n + n * -3n) = 21 (-12n + -3n2) = 21 Solving -12n + -3n2 = 21 Solving for variable 'n'. Reorder the terms: -21 + -12n + -3n2 = 21 + -21 Combine like terms: 21 + -21 = 0 -21 + -12n + -3n2 = 0 Factor out the Greatest Common Factor (GCF), '-3'. -3(7 + 4n + n2) = 0 Ignore the factor -3.Subproblem 1
Set the factor '(7 + 4n + n2)' equal to zero and attempt to solve: Simplifying 7 + 4n + n2 = 0 Solving 7 + 4n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + 4n + -7 + n2 = 0 + -7 Reorder the terms: 7 + -7 + 4n + n2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 4n + n2 = 0 + -7 4n + n2 = 0 + -7 Combine like terms: 0 + -7 = -7 4n + n2 = -7 The n term is 4n. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4n + 4 + n2 = -7 + 4 Reorder the terms: 4 + 4n + n2 = -7 + 4 Combine like terms: -7 + 4 = -3 4 + 4n + n2 = -3 Factor a perfect square on the left side: (n + 2)(n + 2) = -3 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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