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Simplifying 0 = 0.0232x2 + -2.28x + 60.0 Reorder the terms: 0 = 60.0 + -2.28x + 0.0232x2 Solving 0 = 60.0 + -2.28x + 0.0232x2 Solving for variable 'x'. Combine like terms: 0 + -60.0 = -60 -60 + 2.28x + -0.0232x2 = 60.0 + -2.28x + 0.0232x2 + -60.0 + 2.28x + -0.0232x2 Reorder the terms: -60 + 2.28x + -0.0232x2 = 60.0 + -60.0 + -2.28x + 2.28x + 0.0232x2 + -0.0232x2 Combine like terms: 60.0 + -60.0 = 0.0 -60 + 2.28x + -0.0232x2 = 0.0 + -2.28x + 2.28x + 0.0232x2 + -0.0232x2 -60 + 2.28x + -0.0232x2 = -2.28x + 2.28x + 0.0232x2 + -0.0232x2 Combine like terms: -2.28x + 2.28x = 0.00 -60 + 2.28x + -0.0232x2 = 0.00 + 0.0232x2 + -0.0232x2 -60 + 2.28x + -0.0232x2 = 0.0232x2 + -0.0232x2 Combine like terms: 0.0232x2 + -0.0232x2 = 0.0000 -60 + 2.28x + -0.0232x2 = 0.0000 Begin completing the square. Divide all terms by -0.0232 the coefficient of the squared term: Divide each side by '-0.0232'. 2586.206897 + -98.27586207x + x2 = 0 Move the constant term to the right: Add '-2586.206897' to each side of the equation. 2586.206897 + -98.27586207x + -2586.206897 + x2 = 0 + -2586.206897 Reorder the terms: 2586.206897 + -2586.206897 + -98.27586207x + x2 = 0 + -2586.206897 Combine like terms: 2586.206897 + -2586.206897 = 0.000000 0.000000 + -98.27586207x + x2 = 0 + -2586.206897 -98.27586207x + x2 = 0 + -2586.206897 Combine like terms: 0 + -2586.206897 = -2586.206897 -98.27586207x + x2 = -2586.206897 The x term is -98.27586207x. Take half its coefficient (-49.13793104). Square it (2414.536267) and add it to both sides. Add '2414.536267' to each side of the equation. -98.27586207x + 2414.536267 + x2 = -2586.206897 + 2414.536267 Reorder the terms: 2414.536267 + -98.27586207x + x2 = -2586.206897 + 2414.536267 Combine like terms: -2586.206897 + 2414.536267 = -171.67063 2414.536267 + -98.27586207x + x2 = -171.67063 Factor a perfect square on the left side: (x + -49.13793104)(x + -49.13793104) = -171.67063 Can't calculate square root of the right side. The solution to this equation could not be determined.
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