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Simplifying 5n2 + 100 = 30n Reorder the terms: 100 + 5n2 = 30n Solving 100 + 5n2 = 30n Solving for variable 'n'. Reorder the terms: 100 + -30n + 5n2 = 30n + -30n Combine like terms: 30n + -30n = 0 100 + -30n + 5n2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(20 + -6n + n2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(20 + -6n + n2)' equal to zero and attempt to solve: Simplifying 20 + -6n + n2 = 0 Solving 20 + -6n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-20' to each side of the equation. 20 + -6n + -20 + n2 = 0 + -20 Reorder the terms: 20 + -20 + -6n + n2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -6n + n2 = 0 + -20 -6n + n2 = 0 + -20 Combine like terms: 0 + -20 = -20 -6n + n2 = -20 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 = -20 + 9 Reorder the terms: 9 + -6n + n2 = -20 + 9 Combine like terms: -20 + 9 = -11 9 + -6n + n2 = -11 Factor a perfect square on the left side: (n + -3)(n + -3) = -11 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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