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Simplifying 0 = 2X2 + 9X + 12 Reorder the terms: 0 = 12 + 9X + 2X2 Solving 0 = 12 + 9X + 2X2 Solving for variable 'X'. Combine like terms: 0 + -12 = -12 -12 + -9X + -2X2 = 12 + 9X + 2X2 + -12 + -9X + -2X2 Reorder the terms: -12 + -9X + -2X2 = 12 + -12 + 9X + -9X + 2X2 + -2X2 Combine like terms: 12 + -12 = 0 -12 + -9X + -2X2 = 0 + 9X + -9X + 2X2 + -2X2 -12 + -9X + -2X2 = 9X + -9X + 2X2 + -2X2 Combine like terms: 9X + -9X = 0 -12 + -9X + -2X2 = 0 + 2X2 + -2X2 -12 + -9X + -2X2 = 2X2 + -2X2 Combine like terms: 2X2 + -2X2 = 0 -12 + -9X + -2X2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(12 + 9X + 2X2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(12 + 9X + 2X2)' equal to zero and attempt to solve: Simplifying 12 + 9X + 2X2 = 0 Solving 12 + 9X + 2X2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 6 + 4.5X + X2 = 0 Move the constant term to the right: Add '-6' to each side of the equation. 6 + 4.5X + -6 + X2 = 0 + -6 Reorder the terms: 6 + -6 + 4.5X + X2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 4.5X + X2 = 0 + -6 4.5X + X2 = 0 + -6 Combine like terms: 0 + -6 = -6 4.5X + X2 = -6 The X term is 4.5X. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5X + 5.0625 + X2 = -6 + 5.0625 Reorder the terms: 5.0625 + 4.5X + X2 = -6 + 5.0625 Combine like terms: -6 + 5.0625 = -0.9375 5.0625 + 4.5X + X2 = -0.9375 Factor a perfect square on the left side: (X + 2.25)(X + 2.25) = -0.9375 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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