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Simplifying 24x2 + 30x(ln(x) + 1) + -30(ln(x) + 1) + 106x + -130 = 0 Multiply ln * x 24x2 + 30x(lnx + 1) + -30(ln(x) + 1) + 106x + -130 = 0 Reorder the terms: 24x2 + 30x(1 + lnx) + -30(ln(x) + 1) + 106x + -130 = 0 24x2 + (1 * 30x + lnx * 30x) + -30(ln(x) + 1) + 106x + -130 = 0 Reorder the terms: 24x2 + (30lnx2 + 30x) + -30(ln(x) + 1) + 106x + -130 = 0 24x2 + (30lnx2 + 30x) + -30(ln(x) + 1) + 106x + -130 = 0 Multiply ln * x 24x2 + 30lnx2 + 30x + -30(lnx + 1) + 106x + -130 = 0 Reorder the terms: 24x2 + 30lnx2 + 30x + -30(1 + lnx) + 106x + -130 = 0 24x2 + 30lnx2 + 30x + (1 * -30 + lnx * -30) + 106x + -130 = 0 24x2 + 30lnx2 + 30x + (-30 + -30lnx) + 106x + -130 = 0 Reorder the terms: -30 + -130 + -30lnx + 30lnx2 + 30x + 106x + 24x2 = 0 Combine like terms: -30 + -130 = -160 -160 + -30lnx + 30lnx2 + 30x + 106x + 24x2 = 0 Combine like terms: 30x + 106x = 136x -160 + -30lnx + 30lnx2 + 136x + 24x2 = 0 Solving -160 + -30lnx + 30lnx2 + 136x + 24x2 = 0 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '160' to each side of the equation. -160 + -30lnx + 30lnx2 + 136x + 160 + 24x2 = 0 + 160 Reorder the terms: -160 + 160 + -30lnx + 30lnx2 + 136x + 24x2 = 0 + 160 Combine like terms: -160 + 160 = 0 0 + -30lnx + 30lnx2 + 136x + 24x2 = 0 + 160 -30lnx + 30lnx2 + 136x + 24x2 = 0 + 160 Combine like terms: 0 + 160 = 160 -30lnx + 30lnx2 + 136x + 24x2 = 160 Add '-136x' to each side of the equation. -30lnx + 30lnx2 + 136x + -136x + 24x2 = 160 + -136x Combine like terms: 136x + -136x = 0 -30lnx + 30lnx2 + 0 + 24x2 = 160 + -136x -30lnx + 30lnx2 + 24x2 = 160 + -136x Add '-24x2' to each side of the equation. -30lnx + 30lnx2 + 24x2 + -24x2 = 160 + -136x + -24x2 Combine like terms: 24x2 + -24x2 = 0 -30lnx + 30lnx2 + 0 = 160 + -136x + -24x2 -30lnx + 30lnx2 = 160 + -136x + -24x2 Reorder the terms: -160 + -30lnx + 30lnx2 + 136x + 24x2 = 160 + -136x + -24x2 + -160 + 136x + 24x2 Reorder the terms: -160 + -30lnx + 30lnx2 + 136x + 24x2 = 160 + -160 + -136x + 136x + -24x2 + 24x2 Combine like terms: 160 + -160 = 0 -160 + -30lnx + 30lnx2 + 136x + 24x2 = 0 + -136x + 136x + -24x2 + 24x2 -160 + -30lnx + 30lnx2 + 136x + 24x2 = -136x + 136x + -24x2 + 24x2 Combine like terms: -136x + 136x = 0 -160 + -30lnx + 30lnx2 + 136x + 24x2 = 0 + -24x2 + 24x2 -160 + -30lnx + 30lnx2 + 136x + 24x2 = -24x2 + 24x2 Combine like terms: -24x2 + 24x2 = 0 -160 + -30lnx + 30lnx2 + 136x + 24x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-80 + -15lnx + 15lnx2 + 68x + 12x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-80 + -15lnx + 15lnx2 + 68x + 12x2)' equal to zero and attempt to solve: Simplifying -80 + -15lnx + 15lnx2 + 68x + 12x2 = 0 Solving -80 + -15lnx + 15lnx2 + 68x + 12x2 = 0 Move all terms containing l to the left, all other terms to the right. Add '80' to each side of the equation. -80 + -15lnx + 15lnx2 + 68x + 80 + 12x2 = 0 + 80 Reorder the terms: -80 + 80 + -15lnx + 15lnx2 + 68x + 12x2 = 0 + 80 Combine like terms: -80 + 80 = 0 0 + -15lnx + 15lnx2 + 68x + 12x2 = 0 + 80 -15lnx + 15lnx2 + 68x + 12x2 = 0 + 80 Combine like terms: 0 + 80 = 80 -15lnx + 15lnx2 + 68x + 12x2 = 80 Add '-68x' to each side of the equation. -15lnx + 15lnx2 + 68x + -68x + 12x2 = 80 + -68x Combine like terms: 68x + -68x = 0 -15lnx + 15lnx2 + 0 + 12x2 = 80 + -68x -15lnx + 15lnx2 + 12x2 = 80 + -68x Add '-12x2' to each side of the equation. -15lnx + 15lnx2 + 12x2 + -12x2 = 80 + -68x + -12x2 Combine like terms: 12x2 + -12x2 = 0 -15lnx + 15lnx2 + 0 = 80 + -68x + -12x2 -15lnx + 15lnx2 = 80 + -68x + -12x2 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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