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Simplifying 4(2x + -3) * 3 + -1(2x + -3)(4x * 2 + -6x + 9) = 18x + -3 Reorder the terms: 4(-3 + 2x) * 3 + -1(2x + -3)(4x * 2 + -6x + 9) = 18x + -3 Reorder the terms for easier multiplication: 4 * 3(-3 + 2x) + -1(2x + -3)(4x * 2 + -6x + 9) = 18x + -3 Multiply 4 * 3 12(-3 + 2x) + -1(2x + -3)(4x * 2 + -6x + 9) = 18x + -3 (-3 * 12 + 2x * 12) + -1(2x + -3)(4x * 2 + -6x + 9) = 18x + -3 (-36 + 24x) + -1(2x + -3)(4x * 2 + -6x + 9) = 18x + -3 Reorder the terms: -36 + 24x + -1(-3 + 2x)(4x * 2 + -6x + 9) = 18x + -3 Reorder the terms for easier multiplication: -36 + 24x + -1(-3 + 2x)(4 * 2x + -6x + 9) = 18x + -3 Multiply 4 * 2 -36 + 24x + -1(-3 + 2x)(8x + -6x + 9) = 18x + -3 Reorder the terms: -36 + 24x + -1(-3 + 2x)(9 + 8x + -6x) = 18x + -3 Combine like terms: 8x + -6x = 2x -36 + 24x + -1(-3 + 2x)(9 + 2x) = 18x + -3 Multiply (-3 + 2x) * (9 + 2x) -36 + 24x + -1(-3(9 + 2x) + 2x * (9 + 2x)) = 18x + -3 -36 + 24x + -1((9 * -3 + 2x * -3) + 2x * (9 + 2x)) = 18x + -3 -36 + 24x + -1((-27 + -6x) + 2x * (9 + 2x)) = 18x + -3 -36 + 24x + -1(-27 + -6x + (9 * 2x + 2x * 2x)) = 18x + -3 -36 + 24x + -1(-27 + -6x + (18x + 4x2)) = 18x + -3 Combine like terms: -6x + 18x = 12x -36 + 24x + -1(-27 + 12x + 4x2) = 18x + -3 -36 + 24x + (-27 * -1 + 12x * -1 + 4x2 * -1) = 18x + -3 -36 + 24x + (27 + -12x + -4x2) = 18x + -3 Reorder the terms: -36 + 27 + 24x + -12x + -4x2 = 18x + -3 Combine like terms: -36 + 27 = -9 -9 + 24x + -12x + -4x2 = 18x + -3 Combine like terms: 24x + -12x = 12x -9 + 12x + -4x2 = 18x + -3 Reorder the terms: -9 + 12x + -4x2 = -3 + 18x Solving -9 + 12x + -4x2 = -3 + 18x Solving for variable 'x'. Reorder the terms: -9 + 3 + 12x + -18x + -4x2 = -3 + 18x + 3 + -18x Combine like terms: -9 + 3 = -6 -6 + 12x + -18x + -4x2 = -3 + 18x + 3 + -18x Combine like terms: 12x + -18x = -6x -6 + -6x + -4x2 = -3 + 18x + 3 + -18x Reorder the terms: -6 + -6x + -4x2 = -3 + 3 + 18x + -18x Combine like terms: -3 + 3 = 0 -6 + -6x + -4x2 = 0 + 18x + -18x -6 + -6x + -4x2 = 18x + -18x Combine like terms: 18x + -18x = 0 -6 + -6x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(3 + 3x + 2x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(3 + 3x + 2x2)' equal to zero and attempt to solve: Simplifying 3 + 3x + 2x2 = 0 Solving 3 + 3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1.5 + 1.5x + x2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + 1.5x + -1.5 + x2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + 1.5x + x2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + 1.5x + x2 = 0 + -1.5 1.5x + x2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 1.5x + x2 = -1.5 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 = -1.5 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = -1.5 + 0.5625 Combine like terms: -1.5 + 0.5625 = -0.9375 0.5625 + 1.5x + x2 = -0.9375 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = -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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