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Simplifying 6(4x2 + -4x + 1) = 0 Reorder the terms: 6(1 + -4x + 4x2) = 0 (1 * 6 + -4x * 6 + 4x2 * 6) = 0 (6 + -24x + 24x2) = 0 Solving 6 + -24x + 24x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(1 + -4x + 4x2) = 0 Factor a trinomial. 6((1 + -2x)(1 + -2x)) = 0 Ignore the factor 6.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 + -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 = 0.5Solution
x = {0.5, 0.5}
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