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Simplifying 500 = -0.1x2 + 1.1x + 3 Reorder the terms: 500 = 3 + 1.1x + -0.1x2 Solving 500 = 3 + 1.1x + -0.1x2 Solving for variable 'x'. Combine like terms: 500 + -3 = 497 497 + -1.1x + 0.1x2 = 3 + 1.1x + -0.1x2 + -3 + -1.1x + 0.1x2 Reorder the terms: 497 + -1.1x + 0.1x2 = 3 + -3 + 1.1x + -1.1x + -0.1x2 + 0.1x2 Combine like terms: 3 + -3 = 0 497 + -1.1x + 0.1x2 = 0 + 1.1x + -1.1x + -0.1x2 + 0.1x2 497 + -1.1x + 0.1x2 = 1.1x + -1.1x + -0.1x2 + 0.1x2 Combine like terms: 1.1x + -1.1x = 0.0 497 + -1.1x + 0.1x2 = 0.0 + -0.1x2 + 0.1x2 497 + -1.1x + 0.1x2 = -0.1x2 + 0.1x2 Combine like terms: -0.1x2 + 0.1x2 = 0.0 497 + -1.1x + 0.1x2 = 0.0 Begin completing the square. Divide all terms by 0.1 the coefficient of the squared term: Divide each side by '0.1'. 4970 + -11x + x2 = 0 Move the constant term to the right: Add '-4970' to each side of the equation. 4970 + -11x + -4970 + x2 = 0 + -4970 Reorder the terms: 4970 + -4970 + -11x + x2 = 0 + -4970 Combine like terms: 4970 + -4970 = 0 0 + -11x + x2 = 0 + -4970 -11x + x2 = 0 + -4970 Combine like terms: 0 + -4970 = -4970 -11x + x2 = -4970 The x term is -11x. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11x + 30.25 + x2 = -4970 + 30.25 Reorder the terms: 30.25 + -11x + x2 = -4970 + 30.25 Combine like terms: -4970 + 30.25 = -4939.75 30.25 + -11x + x2 = -4939.75 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = -4939.75 Can't calculate square root of the right side. The solution to this equation could not be determined.
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