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Simplifying 0 = -2.11x2 + 0.96x + -0.53 Reorder the terms: 0 = -0.53 + 0.96x + -2.11x2 Solving 0 = -0.53 + 0.96x + -2.11x2 Solving for variable 'x'. Combine like terms: 0 + 0.53 = 0.53 0.53 + -0.96x + 2.11x2 = -0.53 + 0.96x + -2.11x2 + 0.53 + -0.96x + 2.11x2 Reorder the terms: 0.53 + -0.96x + 2.11x2 = -0.53 + 0.53 + 0.96x + -0.96x + -2.11x2 + 2.11x2 Combine like terms: -0.53 + 0.53 = 0.00 0.53 + -0.96x + 2.11x2 = 0.00 + 0.96x + -0.96x + -2.11x2 + 2.11x2 0.53 + -0.96x + 2.11x2 = 0.96x + -0.96x + -2.11x2 + 2.11x2 Combine like terms: 0.96x + -0.96x = 0.00 0.53 + -0.96x + 2.11x2 = 0.00 + -2.11x2 + 2.11x2 0.53 + -0.96x + 2.11x2 = -2.11x2 + 2.11x2 Combine like terms: -2.11x2 + 2.11x2 = 0.00 0.53 + -0.96x + 2.11x2 = 0.00 Begin completing the square. Divide all terms by 2.11 the coefficient of the squared term: Divide each side by '2.11'. 0.2511848341 + -0.4549763033x + x2 = 0 Move the constant term to the right: Add '-0.2511848341' to each side of the equation. 0.2511848341 + -0.4549763033x + -0.2511848341 + x2 = 0 + -0.2511848341 Reorder the terms: 0.2511848341 + -0.2511848341 + -0.4549763033x + x2 = 0 + -0.2511848341 Combine like terms: 0.2511848341 + -0.2511848341 = 0.0000000000 0.0000000000 + -0.4549763033x + x2 = 0 + -0.2511848341 -0.4549763033x + x2 = 0 + -0.2511848341 Combine like terms: 0 + -0.2511848341 = -0.2511848341 -0.4549763033x + x2 = -0.2511848341 The x term is -0.4549763033x. Take half its coefficient (-0.2274881517). Square it (0.05175085916) and add it to both sides. Add '0.05175085916' to each side of the equation. -0.4549763033x + 0.05175085916 + x2 = -0.2511848341 + 0.05175085916 Reorder the terms: 0.05175085916 + -0.4549763033x + x2 = -0.2511848341 + 0.05175085916 Combine like terms: -0.2511848341 + 0.05175085916 = -0.19943397494 0.05175085916 + -0.4549763033x + x2 = -0.19943397494 Factor a perfect square on the left side: (x + -0.2274881517)(x + -0.2274881517) = -0.19943397494 Can't calculate square root of the right side. The solution to this equation could not be determined.
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