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Simplifying 12x2 = 18x + -36 Reorder the terms: 12x2 = -36 + 18x Solving 12x2 = -36 + 18x Solving for variable 'x'. Reorder the terms: 36 + -18x + 12x2 = -36 + 18x + 36 + -18x Reorder the terms: 36 + -18x + 12x2 = -36 + 36 + 18x + -18x Combine like terms: -36 + 36 = 0 36 + -18x + 12x2 = 0 + 18x + -18x 36 + -18x + 12x2 = 18x + -18x Combine like terms: 18x + -18x = 0 36 + -18x + 12x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(6 + -3x + 2x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(6 + -3x + 2x2)' equal to zero and attempt to solve: Simplifying 6 + -3x + 2x2 = 0 Solving 6 + -3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 3 + -1.5x + x2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + -1.5x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + -1.5x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1.5x + x2 = 0 + -3 -1.5x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -1.5x + x2 = -3 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = -3 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = -3 + 0.5625 Combine like terms: -3 + 0.5625 = -2.4375 0.5625 + -1.5x + x2 = -2.4375 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = -2.4375 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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