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Simplifying 478 = -0.5x2 + 36x + -612 Reorder the terms: 478 = -612 + 36x + -0.5x2 Solving 478 = -612 + 36x + -0.5x2 Solving for variable 'x'. Combine like terms: 478 + 612 = 1090 1090 + -36x + 0.5x2 = -612 + 36x + -0.5x2 + 612 + -36x + 0.5x2 Reorder the terms: 1090 + -36x + 0.5x2 = -612 + 612 + 36x + -36x + -0.5x2 + 0.5x2 Combine like terms: -612 + 612 = 0 1090 + -36x + 0.5x2 = 0 + 36x + -36x + -0.5x2 + 0.5x2 1090 + -36x + 0.5x2 = 36x + -36x + -0.5x2 + 0.5x2 Combine like terms: 36x + -36x = 0 1090 + -36x + 0.5x2 = 0 + -0.5x2 + 0.5x2 1090 + -36x + 0.5x2 = -0.5x2 + 0.5x2 Combine like terms: -0.5x2 + 0.5x2 = 0.0 1090 + -36x + 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'. 2180 + -72x + x2 = 0 Move the constant term to the right: Add '-2180' to each side of the equation. 2180 + -72x + -2180 + x2 = 0 + -2180 Reorder the terms: 2180 + -2180 + -72x + x2 = 0 + -2180 Combine like terms: 2180 + -2180 = 0 0 + -72x + x2 = 0 + -2180 -72x + x2 = 0 + -2180 Combine like terms: 0 + -2180 = -2180 -72x + x2 = -2180 The x term is -72x. Take half its coefficient (-36). Square it (1296) and add it to both sides. Add '1296' to each side of the equation. -72x + 1296 + x2 = -2180 + 1296 Reorder the terms: 1296 + -72x + x2 = -2180 + 1296 Combine like terms: -2180 + 1296 = -884 1296 + -72x + x2 = -884 Factor a perfect square on the left side: (x + -36)(x + -36) = -884 Can't calculate square root of the right side. The solution to this equation could not be determined.
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