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Simplifying 24 + -105x = -25x2 + 4 Reorder the terms: 24 + -105x = 4 + -25x2 Solving 24 + -105x = 4 + -25x2 Solving for variable 'x'. Reorder the terms: 24 + -4 + -105x + 25x2 = 4 + -25x2 + -4 + 25x2 Combine like terms: 24 + -4 = 20 20 + -105x + 25x2 = 4 + -25x2 + -4 + 25x2 Reorder the terms: 20 + -105x + 25x2 = 4 + -4 + -25x2 + 25x2 Combine like terms: 4 + -4 = 0 20 + -105x + 25x2 = 0 + -25x2 + 25x2 20 + -105x + 25x2 = -25x2 + 25x2 Combine like terms: -25x2 + 25x2 = 0 20 + -105x + 25x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(4 + -21x + 5x2) = 0 Factor a trinomial. 5((1 + -5x)(4 + -1x)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(1 + -5x)' equal to zero and attempt to solve: Simplifying 1 + -5x = 0 Solving 1 + -5x = 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 + -5x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5x = 0 + -1 -5x = 0 + -1 Combine like terms: 0 + -1 = -1 -5x = -1 Divide each side by '-5'. x = 0.2 Simplifying x = 0.2Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 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 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {0.2, 4}
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