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Simplifying 1.46 = 0.5x2 + x + 12 Reorder the terms: 1.46 = 12 + x + 0.5x2 Solving 1.46 = 12 + x + 0.5x2 Solving for variable 'x'. Combine like terms: 1.46 + -12 = -10.54 -10.54 + -1x + -0.5x2 = 12 + x + 0.5x2 + -12 + -1x + -0.5x2 Reorder the terms: -10.54 + -1x + -0.5x2 = 12 + -12 + x + -1x + 0.5x2 + -0.5x2 Combine like terms: 12 + -12 = 0 -10.54 + -1x + -0.5x2 = 0 + x + -1x + 0.5x2 + -0.5x2 -10.54 + -1x + -0.5x2 = x + -1x + 0.5x2 + -0.5x2 Combine like terms: x + -1x = 0 -10.54 + -1x + -0.5x2 = 0 + 0.5x2 + -0.5x2 -10.54 + -1x + -0.5x2 = 0.5x2 + -0.5x2 Combine like terms: 0.5x2 + -0.5x2 = 0.0 -10.54 + -1x + -0.5x2 = 0.0 Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. 21.08 + 2x + x2 = 0 Move the constant term to the right: Add '-21.08' to each side of the equation. 21.08 + 2x + -21.08 + x2 = 0 + -21.08 Reorder the terms: 21.08 + -21.08 + 2x + x2 = 0 + -21.08 Combine like terms: 21.08 + -21.08 = 0.00 0.00 + 2x + x2 = 0 + -21.08 2x + x2 = 0 + -21.08 Combine like terms: 0 + -21.08 = -21.08 2x + x2 = -21.08 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 = -21.08 + 1 Reorder the terms: 1 + 2x + x2 = -21.08 + 1 Combine like terms: -21.08 + 1 = -20.08 1 + 2x + x2 = -20.08 Factor a perfect square on the left side: (x + 1)(x + 1) = -20.08 Can't calculate square root of the right side. The solution to this equation could not be determined.
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