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Simplifying 8x2 + -6x + 4x + -3 = 48x2 + -27 Reorder the terms: -3 + -6x + 4x + 8x2 = 48x2 + -27 Combine like terms: -6x + 4x = -2x -3 + -2x + 8x2 = 48x2 + -27 Reorder the terms: -3 + -2x + 8x2 = -27 + 48x2 Solving -3 + -2x + 8x2 = -27 + 48x2 Solving for variable 'x'. Reorder the terms: -3 + 27 + -2x + 8x2 + -48x2 = -27 + 48x2 + 27 + -48x2 Combine like terms: -3 + 27 = 24 24 + -2x + 8x2 + -48x2 = -27 + 48x2 + 27 + -48x2 Combine like terms: 8x2 + -48x2 = -40x2 24 + -2x + -40x2 = -27 + 48x2 + 27 + -48x2 Reorder the terms: 24 + -2x + -40x2 = -27 + 27 + 48x2 + -48x2 Combine like terms: -27 + 27 = 0 24 + -2x + -40x2 = 0 + 48x2 + -48x2 24 + -2x + -40x2 = 48x2 + -48x2 Combine like terms: 48x2 + -48x2 = 0 24 + -2x + -40x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(12 + -1x + -20x2) = 0 Factor a trinomial. 2((3 + -4x)(4 + 5x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + -4x)' equal to zero and attempt to solve: Simplifying 3 + -4x = 0 Solving 3 + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -4x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4x = 0 + -3 -4x = 0 + -3 Combine like terms: 0 + -3 = -3 -4x = -3 Divide each side by '-4'. x = 0.75 Simplifying x = 0.75Subproblem 2
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 = -0.8Solution
x = {0.75, -0.8}
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