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Simplifying 9(2 + -3x) * 2x = 8x + -1(x + -23) Reorder the terms for easier multiplication: 9 * 2x(2 + -3x) = 8x + -1(x + -23) Multiply 9 * 2 18x(2 + -3x) = 8x + -1(x + -23) (2 * 18x + -3x * 18x) = 8x + -1(x + -23) (36x + -54x2) = 8x + -1(x + -23) Reorder the terms: 36x + -54x2 = 8x + -1(-23 + x) 36x + -54x2 = 8x + (-23 * -1 + x * -1) 36x + -54x2 = 8x + (23 + -1x) Reorder the terms: 36x + -54x2 = 23 + 8x + -1x Combine like terms: 8x + -1x = 7x 36x + -54x2 = 23 + 7x Solving 36x + -54x2 = 23 + 7x Solving for variable 'x'. Reorder the terms: -23 + 36x + -7x + -54x2 = 23 + 7x + -23 + -7x Combine like terms: 36x + -7x = 29x -23 + 29x + -54x2 = 23 + 7x + -23 + -7x Reorder the terms: -23 + 29x + -54x2 = 23 + -23 + 7x + -7x Combine like terms: 23 + -23 = 0 -23 + 29x + -54x2 = 0 + 7x + -7x -23 + 29x + -54x2 = 7x + -7x Combine like terms: 7x + -7x = 0 -23 + 29x + -54x2 = 0 Begin completing the square. Divide all terms by -54 the coefficient of the squared term: Divide each side by '-54'. 0.4259259259 + -0.537037037x + x2 = 0 Move the constant term to the right: Add '-0.4259259259' to each side of the equation. 0.4259259259 + -0.537037037x + -0.4259259259 + x2 = 0 + -0.4259259259 Reorder the terms: 0.4259259259 + -0.4259259259 + -0.537037037x + x2 = 0 + -0.4259259259 Combine like terms: 0.4259259259 + -0.4259259259 = 0.0000000000 0.0000000000 + -0.537037037x + x2 = 0 + -0.4259259259 -0.537037037x + x2 = 0 + -0.4259259259 Combine like terms: 0 + -0.4259259259 = -0.4259259259 -0.537037037x + x2 = -0.4259259259 The x term is -0.537037037x. Take half its coefficient (-0.2685185185). Square it (0.07210219478) and add it to both sides. Add '0.07210219478' to each side of the equation. -0.537037037x + 0.07210219478 + x2 = -0.4259259259 + 0.07210219478 Reorder the terms: 0.07210219478 + -0.537037037x + x2 = -0.4259259259 + 0.07210219478 Combine like terms: -0.4259259259 + 0.07210219478 = -0.35382373112 0.07210219478 + -0.537037037x + x2 = -0.35382373112 Factor a perfect square on the left side: (x + -0.2685185185)(x + -0.2685185185) = -0.35382373112 Can't calculate square root of the right side. The solution to this equation could not be determined.
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