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Simplifying 0.45 = 0.0021x2 + -0.286x + 16.28 Reorder the terms: 0.45 = 16.28 + -0.286x + 0.0021x2 Solving 0.45 = 16.28 + -0.286x + 0.0021x2 Solving for variable 'x'. Combine like terms: 0.45 + -16.28 = -15.83 -15.83 + 0.286x + -0.0021x2 = 16.28 + -0.286x + 0.0021x2 + -16.28 + 0.286x + -0.0021x2 Reorder the terms: -15.83 + 0.286x + -0.0021x2 = 16.28 + -16.28 + -0.286x + 0.286x + 0.0021x2 + -0.0021x2 Combine like terms: 16.28 + -16.28 = 0.00 -15.83 + 0.286x + -0.0021x2 = 0.00 + -0.286x + 0.286x + 0.0021x2 + -0.0021x2 -15.83 + 0.286x + -0.0021x2 = -0.286x + 0.286x + 0.0021x2 + -0.0021x2 Combine like terms: -0.286x + 0.286x = 0.000 -15.83 + 0.286x + -0.0021x2 = 0.000 + 0.0021x2 + -0.0021x2 -15.83 + 0.286x + -0.0021x2 = 0.0021x2 + -0.0021x2 Combine like terms: 0.0021x2 + -0.0021x2 = 0.0000 -15.83 + 0.286x + -0.0021x2 = 0.0000 Begin completing the square. Divide all terms by -0.0021 the coefficient of the squared term: Divide each side by '-0.0021'. 7538.095238 + -136.1904762x + x2 = 0 Move the constant term to the right: Add '-7538.095238' to each side of the equation. 7538.095238 + -136.1904762x + -7538.095238 + x2 = 0 + -7538.095238 Reorder the terms: 7538.095238 + -7538.095238 + -136.1904762x + x2 = 0 + -7538.095238 Combine like terms: 7538.095238 + -7538.095238 = 0.000000 0.000000 + -136.1904762x + x2 = 0 + -7538.095238 -136.1904762x + x2 = 0 + -7538.095238 Combine like terms: 0 + -7538.095238 = -7538.095238 -136.1904762x + x2 = -7538.095238 The x term is -136.1904762x. Take half its coefficient (-68.0952381). Square it (4636.961452) and add it to both sides. Add '4636.961452' to each side of the equation. -136.1904762x + 4636.961452 + x2 = -7538.095238 + 4636.961452 Reorder the terms: 4636.961452 + -136.1904762x + x2 = -7538.095238 + 4636.961452 Combine like terms: -7538.095238 + 4636.961452 = -2901.133786 4636.961452 + -136.1904762x + x2 = -2901.133786 Factor a perfect square on the left side: (x + -68.0952381)(x + -68.0952381) = -2901.133786 Can't calculate square root of the right side. The solution to this equation could not be determined.
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