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Simplifying 2n2 + -52n + 1000 = 0 Reorder the terms: 1000 + -52n + 2n2 = 0 Solving 1000 + -52n + 2n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2'. 2(500 + -26n + n2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(500 + -26n + n2)' equal to zero and attempt to solve: Simplifying 500 + -26n + n2 = 0 Solving 500 + -26n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-500' to each side of the equation. 500 + -26n + -500 + n2 = 0 + -500 Reorder the terms: 500 + -500 + -26n + n2 = 0 + -500 Combine like terms: 500 + -500 = 0 0 + -26n + n2 = 0 + -500 -26n + n2 = 0 + -500 Combine like terms: 0 + -500 = -500 -26n + n2 = -500 The n term is -26n. Take half its coefficient (-13). Square it (169) and add it to both sides. Add '169' to each side of the equation. -26n + 169 + n2 = -500 + 169 Reorder the terms: 169 + -26n + n2 = -500 + 169 Combine like terms: -500 + 169 = -331 169 + -26n + n2 = -331 Factor a perfect square on the left side: (n + -13)(n + -13) = -331 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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