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Simplifying 5400 + 300n + -50n2 = 7000 Solving 5400 + 300n + -50n2 = 7000 Solving for variable 'n'. Reorder the terms: 5400 + -7000 + 300n + -50n2 = 7000 + -7000 Combine like terms: 5400 + -7000 = -1600 -1600 + 300n + -50n2 = 7000 + -7000 Combine like terms: 7000 + -7000 = 0 -1600 + 300n + -50n2 = 0 Factor out the Greatest Common Factor (GCF), '50'. 50(-32 + 6n + -1n2) = 0 Ignore the factor 50.Subproblem 1
Set the factor '(-32 + 6n + -1n2)' equal to zero and attempt to solve: Simplifying -32 + 6n + -1n2 = 0 Solving -32 + 6n + -1n2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 32 + -6n + n2 = 0 Move the constant term to the right: Add '-32' to each side of the equation. 32 + -6n + -32 + n2 = 0 + -32 Reorder the terms: 32 + -32 + -6n + n2 = 0 + -32 Combine like terms: 32 + -32 = 0 0 + -6n + n2 = 0 + -32 -6n + n2 = 0 + -32 Combine like terms: 0 + -32 = -32 -6n + n2 = -32 The n term is -6n. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6n + 9 + n2 = -32 + 9 Reorder the terms: 9 + -6n + n2 = -32 + 9 Combine like terms: -32 + 9 = -23 9 + -6n + n2 = -23 Factor a perfect square on the left side: (n + -3)(n + -3) = -23 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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