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Simplifying 0 = 2x2 + 3x + 12 Reorder the terms: 0 = 12 + 3x + 2x2 Solving 0 = 12 + 3x + 2x2 Solving for variable 'x'. Combine like terms: 0 + -12 = -12 -12 + -3x + -2x2 = 12 + 3x + 2x2 + -12 + -3x + -2x2 Reorder the terms: -12 + -3x + -2x2 = 12 + -12 + 3x + -3x + 2x2 + -2x2 Combine like terms: 12 + -12 = 0 -12 + -3x + -2x2 = 0 + 3x + -3x + 2x2 + -2x2 -12 + -3x + -2x2 = 3x + -3x + 2x2 + -2x2 Combine like terms: 3x + -3x = 0 -12 + -3x + -2x2 = 0 + 2x2 + -2x2 -12 + -3x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -12 + -3x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(12 + 3x + 2x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(12 + 3x + 2x2)' equal to zero and attempt to solve: Simplifying 12 + 3x + 2x2 = 0 Solving 12 + 3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 6 + 1.5x + x2 = 0 Move the constant term to the right: Add '-6' to each side of the equation. 6 + 1.5x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + 1.5x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 1.5x + x2 = 0 + -6 1.5x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 1.5x + x2 = -6 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 = -6 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = -6 + 0.5625 Combine like terms: -6 + 0.5625 = -5.4375 0.5625 + 1.5x + x2 = -5.4375 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = -5.4375 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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