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Simplifying 0.38 = 0.0021x2 + -0.286x + 16.28 Reorder the terms: 0.38 = 16.28 + -0.286x + 0.0021x2 Solving 0.38 = 16.28 + -0.286x + 0.0021x2 Solving for variable 'x'. Combine like terms: 0.38 + -16.28 = -15.9 -15.9 + 0.286x + -0.0021x2 = 16.28 + -0.286x + 0.0021x2 + -16.28 + 0.286x + -0.0021x2 Reorder the terms: -15.9 + 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 -15.9 + 0.286x + -0.0021x2 = 0.00 + -0.286x + 0.286x + 0.0021x2 + -0.0021x2 -15.9 + 0.286x + -0.0021x2 = -0.286x + 0.286x + 0.0021x2 + -0.0021x2 Combine like terms: -0.286x + 0.286x = 0.000 -15.9 + 0.286x + -0.0021x2 = 0.000 + 0.0021x2 + -0.0021x2 -15.9 + 0.286x + -0.0021x2 = 0.0021x2 + -0.0021x2 Combine like terms: 0.0021x2 + -0.0021x2 = 0.0000 -15.9 + 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'. 7571.428571 + -136.1904762x + x2 = 0 Move the constant term to the right: Add '-7571.428571' to each side of the equation. 7571.428571 + -136.1904762x + -7571.428571 + x2 = 0 + -7571.428571 Reorder the terms: 7571.428571 + -7571.428571 + -136.1904762x + x2 = 0 + -7571.428571 Combine like terms: 7571.428571 + -7571.428571 = 0.000000 0.000000 + -136.1904762x + x2 = 0 + -7571.428571 -136.1904762x + x2 = 0 + -7571.428571 Combine like terms: 0 + -7571.428571 = -7571.428571 -136.1904762x + x2 = -7571.428571 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 = -7571.428571 + 4636.961452 Reorder the terms: 4636.961452 + -136.1904762x + x2 = -7571.428571 + 4636.961452 Combine like terms: -7571.428571 + 4636.961452 = -2934.467119 4636.961452 + -136.1904762x + x2 = -2934.467119 Factor a perfect square on the left side: (x + -68.0952381)(x + -68.0952381) = -2934.467119 Can't calculate square root of the right side. The solution to this equation could not be determined.
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