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Simplifying 0 = 24x2 + -4x + -4 Reorder the terms: 0 = -4 + -4x + 24x2 Solving 0 = -4 + -4x + 24x2 Solving for variable 'x'. Combine like terms: 0 + 4 = 4 4 + 4x + -24x2 = -4 + -4x + 24x2 + 4 + 4x + -24x2 Reorder the terms: 4 + 4x + -24x2 = -4 + 4 + -4x + 4x + 24x2 + -24x2 Combine like terms: -4 + 4 = 0 4 + 4x + -24x2 = 0 + -4x + 4x + 24x2 + -24x2 4 + 4x + -24x2 = -4x + 4x + 24x2 + -24x2 Combine like terms: -4x + 4x = 0 4 + 4x + -24x2 = 0 + 24x2 + -24x2 4 + 4x + -24x2 = 24x2 + -24x2 Combine like terms: 24x2 + -24x2 = 0 4 + 4x + -24x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(1 + x + -6x2) = 0 Factor a trinomial. 4((1 + -2x)(1 + 3x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 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 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5Subproblem 2
Set the factor '(1 + 3x)' equal to zero and attempt to solve: Simplifying 1 + 3x = 0 Solving 1 + 3x = 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 + 3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3x = 0 + -1 3x = 0 + -1 Combine like terms: 0 + -1 = -1 3x = -1 Divide each side by '3'. x = -0.3333333333 Simplifying x = -0.3333333333Solution
x = {0.5, -0.3333333333}
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