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Simplifying 6x(4x2 + -9x + 8) = 0 Reorder the terms: 6x(8 + -9x + 4x2) = 0 (8 * 6x + -9x * 6x + 4x2 * 6x) = 0 (48x + -54x2 + 24x3) = 0 Solving 48x + -54x2 + 24x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6x'. 6x(8 + -9x + 4x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(8 + -9x + 4x2)' equal to zero and attempt to solve: Simplifying 8 + -9x + 4x2 = 0 Solving 8 + -9x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2 + -2.25x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -2.25x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -2.25x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -2.25x + x2 = 0 + -2 -2.25x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -2.25x + x2 = -2 The x term is -2.25x. Take half its coefficient (-1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. -2.25x + 1.265625 + x2 = -2 + 1.265625 Reorder the terms: 1.265625 + -2.25x + x2 = -2 + 1.265625 Combine like terms: -2 + 1.265625 = -0.734375 1.265625 + -2.25x + x2 = -0.734375 Factor a perfect square on the left side: (x + -1.125)(x + -1.125) = -0.734375 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
x = {0}
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