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Simplifying 0 = 2x2 + -12x + 24 Reorder the terms: 0 = 24 + -12x + 2x2 Solving 0 = 24 + -12x + 2x2 Solving for variable 'x'. Combine like terms: 0 + -24 = -24 -24 + 12x + -2x2 = 24 + -12x + 2x2 + -24 + 12x + -2x2 Reorder the terms: -24 + 12x + -2x2 = 24 + -24 + -12x + 12x + 2x2 + -2x2 Combine like terms: 24 + -24 = 0 -24 + 12x + -2x2 = 0 + -12x + 12x + 2x2 + -2x2 -24 + 12x + -2x2 = -12x + 12x + 2x2 + -2x2 Combine like terms: -12x + 12x = 0 -24 + 12x + -2x2 = 0 + 2x2 + -2x2 -24 + 12x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -24 + 12x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-12 + 6x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-12 + 6x + -1x2)' equal to zero and attempt to solve: Simplifying -12 + 6x + -1x2 = 0 Solving -12 + 6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 12 + -6x + x2 = 0 Move the constant term to the right: Add '-12' to each side of the equation. 12 + -6x + -12 + x2 = 0 + -12 Reorder the terms: 12 + -12 + -6x + x2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -6x + x2 = 0 + -12 -6x + x2 = 0 + -12 Combine like terms: 0 + -12 = -12 -6x + x2 = -12 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = -12 + 9 Reorder the terms: 9 + -6x + x2 = -12 + 9 Combine like terms: -12 + 9 = -3 9 + -6x + x2 = -3 Factor a perfect square on the left side: (x + -3)(x + -3) = -3 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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