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Simplifying 1080 = -2n2 + 2n + 420 Reorder the terms: 1080 = 420 + 2n + -2n2 Solving 1080 = 420 + 2n + -2n2 Solving for variable 'n'. Combine like terms: 1080 + -420 = 660 660 + -2n + 2n2 = 420 + 2n + -2n2 + -420 + -2n + 2n2 Reorder the terms: 660 + -2n + 2n2 = 420 + -420 + 2n + -2n + -2n2 + 2n2 Combine like terms: 420 + -420 = 0 660 + -2n + 2n2 = 0 + 2n + -2n + -2n2 + 2n2 660 + -2n + 2n2 = 2n + -2n + -2n2 + 2n2 Combine like terms: 2n + -2n = 0 660 + -2n + 2n2 = 0 + -2n2 + 2n2 660 + -2n + 2n2 = -2n2 + 2n2 Combine like terms: -2n2 + 2n2 = 0 660 + -2n + 2n2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(330 + -1n + n2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(330 + -1n + n2)' equal to zero and attempt to solve: Simplifying 330 + -1n + n2 = 0 Solving 330 + -1n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-330' to each side of the equation. 330 + -1n + -330 + n2 = 0 + -330 Reorder the terms: 330 + -330 + -1n + n2 = 0 + -330 Combine like terms: 330 + -330 = 0 0 + -1n + n2 = 0 + -330 -1n + n2 = 0 + -330 Combine like terms: 0 + -330 = -330 -1n + n2 = -330 The n term is -1n. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1n + 0.25 + n2 = -330 + 0.25 Reorder the terms: 0.25 + -1n + n2 = -330 + 0.25 Combine like terms: -330 + 0.25 = -329.75 0.25 + -1n + n2 = -329.75 Factor a perfect square on the left side: (n + -0.5)(n + -0.5) = -329.75 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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