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Simplifying 6x2 + 9x + 12 = 0 Reorder the terms: 12 + 9x + 6x2 = 0 Solving 12 + 9x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(4 + 3x + 2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(4 + 3x + 2x2)' equal to zero and attempt to solve: Simplifying 4 + 3x + 2x2 = 0 Solving 4 + 3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2 + 1.5x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + 1.5x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + 1.5x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 1.5x + x2 = 0 + -2 1.5x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 1.5x + x2 = -2 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 = -2 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = -2 + 0.5625 Combine like terms: -2 + 0.5625 = -1.4375 0.5625 + 1.5x + x2 = -1.4375 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = -1.4375 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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