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Simplifying 24x2 = 14 + 50x Solving 24x2 = 14 + 50x Solving for variable 'x'. Reorder the terms: -14 + -50x + 24x2 = 14 + 50x + -14 + -50x Reorder the terms: -14 + -50x + 24x2 = 14 + -14 + 50x + -50x Combine like terms: 14 + -14 = 0 -14 + -50x + 24x2 = 0 + 50x + -50x -14 + -50x + 24x2 = 50x + -50x Combine like terms: 50x + -50x = 0 -14 + -50x + 24x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-7 + -25x + 12x2) = 0 Factor a trinomial. 2((-1 + -4x)(7 + -3x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -4x)' equal to zero and attempt to solve: Simplifying -1 + -4x = 0 Solving -1 + -4x = 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 + -4x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -4x = 0 + 1 -4x = 0 + 1 Combine like terms: 0 + 1 = 1 -4x = 1 Divide each side by '-4'. x = -0.25 Simplifying x = -0.25Subproblem 2
Set the factor '(7 + -3x)' equal to zero and attempt to solve: Simplifying 7 + -3x = 0 Solving 7 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -3x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3x = 0 + -7 -3x = 0 + -7 Combine like terms: 0 + -7 = -7 -3x = -7 Divide each side by '-3'. x = 2.333333333 Simplifying x = 2.333333333Solution
x = {-0.25, 2.333333333}
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