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Simplifying 0 = n2 + 60n + 1600 Reorder the terms: 0 = 1600 + 60n + n2 Solving 0 = 1600 + 60n + n2 Solving for variable 'n'. Combine like terms: 0 + -1600 = -1600 -1600 + -60n + -1n2 = 1600 + 60n + n2 + -1600 + -60n + -1n2 Reorder the terms: -1600 + -60n + -1n2 = 1600 + -1600 + 60n + -60n + n2 + -1n2 Combine like terms: 1600 + -1600 = 0 -1600 + -60n + -1n2 = 0 + 60n + -60n + n2 + -1n2 -1600 + -60n + -1n2 = 60n + -60n + n2 + -1n2 Combine like terms: 60n + -60n = 0 -1600 + -60n + -1n2 = 0 + n2 + -1n2 -1600 + -60n + -1n2 = n2 + -1n2 Combine like terms: n2 + -1n2 = 0 -1600 + -60n + -1n2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(1600 + 60n + n2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(1600 + 60n + n2)' equal to zero and attempt to solve: Simplifying 1600 + 60n + n2 = 0 Solving 1600 + 60n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-1600' to each side of the equation. 1600 + 60n + -1600 + n2 = 0 + -1600 Reorder the terms: 1600 + -1600 + 60n + n2 = 0 + -1600 Combine like terms: 1600 + -1600 = 0 0 + 60n + n2 = 0 + -1600 60n + n2 = 0 + -1600 Combine like terms: 0 + -1600 = -1600 60n + n2 = -1600 The n term is 60n. Take half its coefficient (30). Square it (900) and add it to both sides. Add '900' to each side of the equation. 60n + 900 + n2 = -1600 + 900 Reorder the terms: 900 + 60n + n2 = -1600 + 900 Combine like terms: -1600 + 900 = -700 900 + 60n + n2 = -700 Factor a perfect square on the left side: (n + 30)(n + 30) = -700 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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