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Simplifying 6x(2x + -3) + -3x = 2x + -18 + x Reorder the terms: 6x(-3 + 2x) + -3x = 2x + -18 + x (-3 * 6x + 2x * 6x) + -3x = 2x + -18 + x (-18x + 12x2) + -3x = 2x + -18 + x Reorder the terms: -18x + -3x + 12x2 = 2x + -18 + x Combine like terms: -18x + -3x = -21x -21x + 12x2 = 2x + -18 + x Reorder the terms: -21x + 12x2 = -18 + 2x + x Combine like terms: 2x + x = 3x -21x + 12x2 = -18 + 3x Solving -21x + 12x2 = -18 + 3x Solving for variable 'x'. Reorder the terms: 18 + -21x + -3x + 12x2 = -18 + 3x + 18 + -3x Combine like terms: -21x + -3x = -24x 18 + -24x + 12x2 = -18 + 3x + 18 + -3x Reorder the terms: 18 + -24x + 12x2 = -18 + 18 + 3x + -3x Combine like terms: -18 + 18 = 0 18 + -24x + 12x2 = 0 + 3x + -3x 18 + -24x + 12x2 = 3x + -3x Combine like terms: 3x + -3x = 0 18 + -24x + 12x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(3 + -4x + 2x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(3 + -4x + 2x2)' equal to zero and attempt to solve: Simplifying 3 + -4x + 2x2 = 0 Solving 3 + -4x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1.5 + -2x + x2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -2x + -1.5 + x2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -2x + x2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -2x + x2 = 0 + -1.5 -2x + x2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -2x + x2 = -1.5 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = -1.5 + 1 Reorder the terms: 1 + -2x + x2 = -1.5 + 1 Combine like terms: -1.5 + 1 = -0.5 1 + -2x + x2 = -0.5 Factor a perfect square on the left side: (x + -1)(x + -1) = -0.5 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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