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Simplifying 5x2 + -9x + -3 = 16x + -23 Reorder the terms: -3 + -9x + 5x2 = 16x + -23 Reorder the terms: -3 + -9x + 5x2 = -23 + 16x Solving -3 + -9x + 5x2 = -23 + 16x Solving for variable 'x'. Reorder the terms: -3 + 23 + -9x + -16x + 5x2 = -23 + 16x + 23 + -16x Combine like terms: -3 + 23 = 20 20 + -9x + -16x + 5x2 = -23 + 16x + 23 + -16x Combine like terms: -9x + -16x = -25x 20 + -25x + 5x2 = -23 + 16x + 23 + -16x Reorder the terms: 20 + -25x + 5x2 = -23 + 23 + 16x + -16x Combine like terms: -23 + 23 = 0 20 + -25x + 5x2 = 0 + 16x + -16x 20 + -25x + 5x2 = 16x + -16x Combine like terms: 16x + -16x = 0 20 + -25x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(4 + -5x + x2) = 0 Factor a trinomial. 5((1 + -1x)(4 + -1x)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Subproblem 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 = {1, 4}
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