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Simplifying 21x + 16 = 30x2 + 50x + 20 Reorder the terms: 16 + 21x = 30x2 + 50x + 20 Reorder the terms: 16 + 21x = 20 + 50x + 30x2 Solving 16 + 21x = 20 + 50x + 30x2 Solving for variable 'x'. Reorder the terms: 16 + -20 + 21x + -50x + -30x2 = 20 + 50x + 30x2 + -20 + -50x + -30x2 Combine like terms: 16 + -20 = -4 -4 + 21x + -50x + -30x2 = 20 + 50x + 30x2 + -20 + -50x + -30x2 Combine like terms: 21x + -50x = -29x -4 + -29x + -30x2 = 20 + 50x + 30x2 + -20 + -50x + -30x2 Reorder the terms: -4 + -29x + -30x2 = 20 + -20 + 50x + -50x + 30x2 + -30x2 Combine like terms: 20 + -20 = 0 -4 + -29x + -30x2 = 0 + 50x + -50x + 30x2 + -30x2 -4 + -29x + -30x2 = 50x + -50x + 30x2 + -30x2 Combine like terms: 50x + -50x = 0 -4 + -29x + -30x2 = 0 + 30x2 + -30x2 -4 + -29x + -30x2 = 30x2 + -30x2 Combine like terms: 30x2 + -30x2 = 0 -4 + -29x + -30x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(4 + 29x + 30x2) = 0 Factor a trinomial. -1((4 + 5x)(1 + 6x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(4 + 5x)' equal to zero and attempt to solve: Simplifying 4 + 5x = 0 Solving 4 + 5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 5x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 5x = 0 + -4 5x = 0 + -4 Combine like terms: 0 + -4 = -4 5x = -4 Divide each side by '5'. x = -0.8 Simplifying x = -0.8Subproblem 2
Set the factor '(1 + 6x)' equal to zero and attempt to solve: Simplifying 1 + 6x = 0 Solving 1 + 6x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 6x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 6x = 0 + -1 6x = 0 + -1 Combine like terms: 0 + -1 = -1 6x = -1 Divide each side by '6'. x = -0.1666666667 Simplifying x = -0.1666666667Solution
x = {-0.8, -0.1666666667}
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