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Simplifying 36x2 = 21 + 75x Solving 36x2 = 21 + 75x Solving for variable 'x'. Reorder the terms: -21 + -75x + 36x2 = 21 + 75x + -21 + -75x Reorder the terms: -21 + -75x + 36x2 = 21 + -21 + 75x + -75x Combine like terms: 21 + -21 = 0 -21 + -75x + 36x2 = 0 + 75x + -75x -21 + -75x + 36x2 = 75x + -75x Combine like terms: 75x + -75x = 0 -21 + -75x + 36x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-7 + -25x + 12x2) = 0 Factor a trinomial. 3((-1 + -4x)(7 + -3x)) = 0 Ignore the factor 3.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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