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Simplifying 3y + -1y + -4 = 18y2 + -9y + 20 Reorder the terms: -4 + 3y + -1y = 18y2 + -9y + 20 Combine like terms: 3y + -1y = 2y -4 + 2y = 18y2 + -9y + 20 Reorder the terms: -4 + 2y = 20 + -9y + 18y2 Solving -4 + 2y = 20 + -9y + 18y2 Solving for variable 'y'. Reorder the terms: -4 + -20 + 2y + 9y + -18y2 = 20 + -9y + 18y2 + -20 + 9y + -18y2 Combine like terms: -4 + -20 = -24 -24 + 2y + 9y + -18y2 = 20 + -9y + 18y2 + -20 + 9y + -18y2 Combine like terms: 2y + 9y = 11y -24 + 11y + -18y2 = 20 + -9y + 18y2 + -20 + 9y + -18y2 Reorder the terms: -24 + 11y + -18y2 = 20 + -20 + -9y + 9y + 18y2 + -18y2 Combine like terms: 20 + -20 = 0 -24 + 11y + -18y2 = 0 + -9y + 9y + 18y2 + -18y2 -24 + 11y + -18y2 = -9y + 9y + 18y2 + -18y2 Combine like terms: -9y + 9y = 0 -24 + 11y + -18y2 = 0 + 18y2 + -18y2 -24 + 11y + -18y2 = 18y2 + -18y2 Combine like terms: 18y2 + -18y2 = 0 -24 + 11y + -18y2 = 0 Begin completing the square. Divide all terms by -18 the coefficient of the squared term: Divide each side by '-18'. 1.333333333 + -0.6111111111y + y2 = 0 Move the constant term to the right: Add '-1.333333333' to each side of the equation. 1.333333333 + -0.6111111111y + -1.333333333 + y2 = 0 + -1.333333333 Reorder the terms: 1.333333333 + -1.333333333 + -0.6111111111y + y2 = 0 + -1.333333333 Combine like terms: 1.333333333 + -1.333333333 = 0.000000000 0.000000000 + -0.6111111111y + y2 = 0 + -1.333333333 -0.6111111111y + y2 = 0 + -1.333333333 Combine like terms: 0 + -1.333333333 = -1.333333333 -0.6111111111y + y2 = -1.333333333 The y term is -0.6111111111y. Take half its coefficient (-0.3055555556). Square it (0.09336419756) and add it to both sides. Add '0.09336419756' to each side of the equation. -0.6111111111y + 0.09336419756 + y2 = -1.333333333 + 0.09336419756 Reorder the terms: 0.09336419756 + -0.6111111111y + y2 = -1.333333333 + 0.09336419756 Combine like terms: -1.333333333 + 0.09336419756 = -1.23996913544 0.09336419756 + -0.6111111111y + y2 = -1.23996913544 Factor a perfect square on the left side: (y + -0.3055555556)(y + -0.3055555556) = -1.23996913544 Can't calculate square root of the right side. The solution to this equation could not be determined.
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