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Simplifying -11n(6n + 4) = 5n + 9(n + 4) Reorder the terms: -11n(4 + 6n) = 5n + 9(n + 4) (4 * -11n + 6n * -11n) = 5n + 9(n + 4) (-44n + -66n2) = 5n + 9(n + 4) Reorder the terms: -44n + -66n2 = 5n + 9(4 + n) -44n + -66n2 = 5n + (4 * 9 + n * 9) -44n + -66n2 = 5n + (36 + 9n) Reorder the terms: -44n + -66n2 = 36 + 5n + 9n Combine like terms: 5n + 9n = 14n -44n + -66n2 = 36 + 14n Solving -44n + -66n2 = 36 + 14n Solving for variable 'n'. Reorder the terms: -36 + -44n + -14n + -66n2 = 36 + 14n + -36 + -14n Combine like terms: -44n + -14n = -58n -36 + -58n + -66n2 = 36 + 14n + -36 + -14n Reorder the terms: -36 + -58n + -66n2 = 36 + -36 + 14n + -14n Combine like terms: 36 + -36 = 0 -36 + -58n + -66n2 = 0 + 14n + -14n -36 + -58n + -66n2 = 14n + -14n Combine like terms: 14n + -14n = 0 -36 + -58n + -66n2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(18 + 29n + 33n2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(18 + 29n + 33n2)' equal to zero and attempt to solve: Simplifying 18 + 29n + 33n2 = 0 Solving 18 + 29n + 33n2 = 0 Begin completing the square. Divide all terms by 33 the coefficient of the squared term: Divide each side by '33'. 0.5454545455 + 0.8787878788n + n2 = 0 Move the constant term to the right: Add '-0.5454545455' to each side of the equation. 0.5454545455 + 0.8787878788n + -0.5454545455 + n2 = 0 + -0.5454545455 Reorder the terms: 0.5454545455 + -0.5454545455 + 0.8787878788n + n2 = 0 + -0.5454545455 Combine like terms: 0.5454545455 + -0.5454545455 = 0.0000000000 0.0000000000 + 0.8787878788n + n2 = 0 + -0.5454545455 0.8787878788n + n2 = 0 + -0.5454545455 Combine like terms: 0 + -0.5454545455 = -0.5454545455 0.8787878788n + n2 = -0.5454545455 The n term is 0.8787878788n. Take half its coefficient (0.4393939394). Square it (0.1930670340) and add it to both sides. Add '0.1930670340' to each side of the equation. 0.8787878788n + 0.1930670340 + n2 = -0.5454545455 + 0.1930670340 Reorder the terms: 0.1930670340 + 0.8787878788n + n2 = -0.5454545455 + 0.1930670340 Combine like terms: -0.5454545455 + 0.1930670340 = -0.3523875115 0.1930670340 + 0.8787878788n + n2 = -0.3523875115 Factor a perfect square on the left side: (n + 0.4393939394)(n + 0.4393939394) = -0.3523875115 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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