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Simplifying -6n(-1 + 7n) + -10n(4 + 3n) + -6(2 + -7n) + -2(-3n + -2) = 0 (-1 * -6n + 7n * -6n) + -10n(4 + 3n) + -6(2 + -7n) + -2(-3n + -2) = 0 (6n + -42n2) + -10n(4 + 3n) + -6(2 + -7n) + -2(-3n + -2) = 0 6n + -42n2 + (4 * -10n + 3n * -10n) + -6(2 + -7n) + -2(-3n + -2) = 0 6n + -42n2 + (-40n + -30n2) + -6(2 + -7n) + -2(-3n + -2) = 0 6n + -42n2 + -40n + -30n2 + (2 * -6 + -7n * -6) + -2(-3n + -2) = 0 6n + -42n2 + -40n + -30n2 + (-12 + 42n) + -2(-3n + -2) = 0 Reorder the terms: 6n + -42n2 + -40n + -30n2 + -12 + 42n + -2(-2 + -3n) = 0 6n + -42n2 + -40n + -30n2 + -12 + 42n + (-2 * -2 + -3n * -2) = 0 6n + -42n2 + -40n + -30n2 + -12 + 42n + (4 + 6n) = 0 Reorder the terms: -12 + 4 + 6n + -40n + 42n + 6n + -42n2 + -30n2 = 0 Combine like terms: -12 + 4 = -8 -8 + 6n + -40n + 42n + 6n + -42n2 + -30n2 = 0 Combine like terms: 6n + -40n = -34n -8 + -34n + 42n + 6n + -42n2 + -30n2 = 0 Combine like terms: -34n + 42n = 8n -8 + 8n + 6n + -42n2 + -30n2 = 0 Combine like terms: 8n + 6n = 14n -8 + 14n + -42n2 + -30n2 = 0 Combine like terms: -42n2 + -30n2 = -72n2 -8 + 14n + -72n2 = 0 Solving -8 + 14n + -72n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + 7n + -36n2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + 7n + -36n2)' equal to zero and attempt to solve: Simplifying -4 + 7n + -36n2 = 0 Solving -4 + 7n + -36n2 = 0 Begin completing the square. Divide all terms by -36 the coefficient of the squared term: Divide each side by '-36'. 0.1111111111 + -0.1944444444n + n2 = 0 Move the constant term to the right: Add '-0.1111111111' to each side of the equation. 0.1111111111 + -0.1944444444n + -0.1111111111 + n2 = 0 + -0.1111111111 Reorder the terms: 0.1111111111 + -0.1111111111 + -0.1944444444n + n2 = 0 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + -0.1944444444n + n2 = 0 + -0.1111111111 -0.1944444444n + n2 = 0 + -0.1111111111 Combine like terms: 0 + -0.1111111111 = -0.1111111111 -0.1944444444n + n2 = -0.1111111111 The n term is -0.1944444444n. Take half its coefficient (-0.0972222222). Square it (0.009452160490) and add it to both sides. Add '0.009452160490' to each side of the equation. -0.1944444444n + 0.009452160490 + n2 = -0.1111111111 + 0.009452160490 Reorder the terms: 0.009452160490 + -0.1944444444n + n2 = -0.1111111111 + 0.009452160490 Combine like terms: -0.1111111111 + 0.009452160490 = -0.10165895061 0.009452160490 + -0.1944444444n + n2 = -0.10165895061 Factor a perfect square on the left side: (n + -0.0972222222)(n + -0.0972222222) = -0.10165895061 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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