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Simplifying 5 = 3x(1 + -2x) 5 = (1 * 3x + -2x * 3x) 5 = (3x + -6x2) Solving 5 = 3x + -6x2 Solving for variable 'x'. Reorder the terms: 5 + -3x + 6x2 = 3x + -3x + -6x2 + 6x2 Combine like terms: 3x + -3x = 0 5 + -3x + 6x2 = 0 + -6x2 + 6x2 5 + -3x + 6x2 = -6x2 + 6x2 Combine like terms: -6x2 + 6x2 = 0 5 + -3x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.8333333333 + -0.5x + x2 = 0 Move the constant term to the right: Add '-0.8333333333' to each side of the equation. 0.8333333333 + -0.5x + -0.8333333333 + x2 = 0 + -0.8333333333 Reorder the terms: 0.8333333333 + -0.8333333333 + -0.5x + x2 = 0 + -0.8333333333 Combine like terms: 0.8333333333 + -0.8333333333 = 0.0000000000 0.0000000000 + -0.5x + x2 = 0 + -0.8333333333 -0.5x + x2 = 0 + -0.8333333333 Combine like terms: 0 + -0.8333333333 = -0.8333333333 -0.5x + x2 = -0.8333333333 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = -0.8333333333 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = -0.8333333333 + 0.0625 Combine like terms: -0.8333333333 + 0.0625 = -0.7708333333 0.0625 + -0.5x + x2 = -0.7708333333 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = -0.7708333333 Can't calculate square root of the right side. The solution to this equation could not be determined.
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