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Simplifying 0.5(x2) + -4x + 3ln(x) = 0 Multiply ln * x 0.5x2 + -4x + 3lnx = 0 Reorder the terms: 3lnx + -4x + 0.5x2 = 0 Solving 3lnx + -4x + 0.5x2 = 0 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '4x' to each side of the equation. 3lnx + -4x + 4x + 0.5x2 = 0 + 4x Combine like terms: -4x + 4x = 0 3lnx + 0 + 0.5x2 = 0 + 4x 3lnx + 0.5x2 = 0 + 4x Remove the zero: 3lnx + 0.5x2 = 4x Add '-0.5x2' to each side of the equation. 3lnx + 0.5x2 + -0.5x2 = 4x + -0.5x2 Combine like terms: 0.5x2 + -0.5x2 = 0.0 3lnx + 0.0 = 4x + -0.5x2 3lnx = 4x + -0.5x2 Divide each side by '3nx'. l = 1.333333333n-1 + -0.1666666667n-1x Simplifying l = 1.333333333n-1 + -0.1666666667n-1x
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