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Simplifying 6x2 + -24x + 27 = 0 Reorder the terms: 27 + -24x + 6x2 = 0 Solving 27 + -24x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(9 + -8x + 2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(9 + -8x + 2x2)' equal to zero and attempt to solve: Simplifying 9 + -8x + 2x2 = 0 Solving 9 + -8x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 4.5 + -4x + x2 = 0 Move the constant term to the right: Add '-4.5' to each side of the equation. 4.5 + -4x + -4.5 + x2 = 0 + -4.5 Reorder the terms: 4.5 + -4.5 + -4x + x2 = 0 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + -4x + x2 = 0 + -4.5 -4x + x2 = 0 + -4.5 Combine like terms: 0 + -4.5 = -4.5 -4x + x2 = -4.5 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = -4.5 + 4 Reorder the terms: 4 + -4x + x2 = -4.5 + 4 Combine like terms: -4.5 + 4 = -0.5 4 + -4x + x2 = -0.5 Factor a perfect square on the left side: (x + -2)(x + -2) = -0.5 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. The solution to this equation could not be determined.
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