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Simplifying 3x + -5 + -0.5x = 1.5x(x + -1) + 3 + -0.5 Reorder the terms: -5 + 3x + -0.5x = 1.5x(x + -1) + 3 + -0.5 Combine like terms: 3x + -0.5x = 2.5x -5 + 2.5x = 1.5x(x + -1) + 3 + -0.5 Reorder the terms: -5 + 2.5x = 1.5x(-1 + x) + 3 + -0.5 -5 + 2.5x = (-1 * 1.5x + x * 1.5x) + 3 + -0.5 -5 + 2.5x = (-1.5x + 1.5x2) + 3 + -0.5 Reorder the terms: -5 + 2.5x = 3 + -0.5 + -1.5x + 1.5x2 Combine like terms: 3 + -0.5 = 2.5 -5 + 2.5x = 2.5 + -1.5x + 1.5x2 Solving -5 + 2.5x = 2.5 + -1.5x + 1.5x2 Solving for variable 'x'. Reorder the terms: -5 + -2.5 + 2.5x + 1.5x + -1.5x2 = 2.5 + -1.5x + 1.5x2 + -2.5 + 1.5x + -1.5x2 Combine like terms: -5 + -2.5 = -7.5 -7.5 + 2.5x + 1.5x + -1.5x2 = 2.5 + -1.5x + 1.5x2 + -2.5 + 1.5x + -1.5x2 Combine like terms: 2.5x + 1.5x = 4x -7.5 + 4x + -1.5x2 = 2.5 + -1.5x + 1.5x2 + -2.5 + 1.5x + -1.5x2 Reorder the terms: -7.5 + 4x + -1.5x2 = 2.5 + -2.5 + -1.5x + 1.5x + 1.5x2 + -1.5x2 Combine like terms: 2.5 + -2.5 = 0.0 -7.5 + 4x + -1.5x2 = 0.0 + -1.5x + 1.5x + 1.5x2 + -1.5x2 -7.5 + 4x + -1.5x2 = -1.5x + 1.5x + 1.5x2 + -1.5x2 Combine like terms: -1.5x + 1.5x = 0.0 -7.5 + 4x + -1.5x2 = 0.0 + 1.5x2 + -1.5x2 -7.5 + 4x + -1.5x2 = 1.5x2 + -1.5x2 Combine like terms: 1.5x2 + -1.5x2 = 0.0 -7.5 + 4x + -1.5x2 = 0.0 Begin completing the square. Divide all terms by -1.5 the coefficient of the squared term: Divide each side by '-1.5'. 5 + -2.666666667x + x2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + -2.666666667x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + -2.666666667x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2.666666667x + x2 = 0 + -5 -2.666666667x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -2.666666667x + x2 = -5 The x term is -2.666666667x. Take half its coefficient (-1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. -2.666666667x + 1.777777780 + x2 = -5 + 1.777777780 Reorder the terms: 1.777777780 + -2.666666667x + x2 = -5 + 1.777777780 Combine like terms: -5 + 1.777777780 = -3.22222222 1.777777780 + -2.666666667x + x2 = -3.22222222 Factor a perfect square on the left side: (x + -1.333333334)(x + -1.333333334) = -3.22222222 Can't calculate square root of the right side. The solution to this equation could not be determined.
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