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Simplifying 5x + 15tx(200 + -20x) = 60 5x + (200 * 15tx + -20x * 15tx) = 60 5x + (3000tx + -300tx2) = 60 Reorder the terms: 3000tx + -300tx2 + 5x = 60 Solving 3000tx + -300tx2 + 5x = 60 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-5x' to each side of the equation. 3000tx + -300tx2 + 5x + -5x = 60 + -5x Combine like terms: 5x + -5x = 0 3000tx + -300tx2 + 0 = 60 + -5x 3000tx + -300tx2 = 60 + -5x Reorder the terms: -60 + 3000tx + -300tx2 + 5x = 60 + -5x + -60 + 5x Reorder the terms: -60 + 3000tx + -300tx2 + 5x = 60 + -60 + -5x + 5x Combine like terms: 60 + -60 = 0 -60 + 3000tx + -300tx2 + 5x = 0 + -5x + 5x -60 + 3000tx + -300tx2 + 5x = -5x + 5x Combine like terms: -5x + 5x = 0 -60 + 3000tx + -300tx2 + 5x = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-12 + 600tx + -60tx2 + x) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-12 + 600tx + -60tx2 + x)' equal to zero and attempt to solve: Simplifying -12 + 600tx + -60tx2 + x = 0 Solving -12 + 600tx + -60tx2 + x = 0 Move all terms containing t to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 600tx + -60tx2 + 12 + x = 0 + 12 Reorder the terms: -12 + 12 + 600tx + -60tx2 + x = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 600tx + -60tx2 + x = 0 + 12 600tx + -60tx2 + x = 0 + 12 Combine like terms: 0 + 12 = 12 600tx + -60tx2 + x = 12 Add '-1x' to each side of the equation. 600tx + -60tx2 + x + -1x = 12 + -1x Combine like terms: x + -1x = 0 600tx + -60tx2 + 0 = 12 + -1x 600tx + -60tx2 = 12 + -1x 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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