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Simplifying x2 + y2 + 2x + -8y + 3k = 0 Reorder the terms: 3k + 2x + x2 + -8y + y2 = 0 Solving 3k + 2x + x2 + -8y + y2 = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-2x' to each side of the equation. 3k + 2x + x2 + -8y + -2x + y2 = 0 + -2x Reorder the terms: 3k + 2x + -2x + x2 + -8y + y2 = 0 + -2x Combine like terms: 2x + -2x = 0 3k + 0 + x2 + -8y + y2 = 0 + -2x 3k + x2 + -8y + y2 = 0 + -2x Remove the zero: 3k + x2 + -8y + y2 = -2x Add '-1x2' to each side of the equation. 3k + x2 + -8y + -1x2 + y2 = -2x + -1x2 Reorder the terms: 3k + x2 + -1x2 + -8y + y2 = -2x + -1x2 Combine like terms: x2 + -1x2 = 0 3k + 0 + -8y + y2 = -2x + -1x2 3k + -8y + y2 = -2x + -1x2 Add '8y' to each side of the equation. 3k + -8y + 8y + y2 = -2x + -1x2 + 8y Combine like terms: -8y + 8y = 0 3k + 0 + y2 = -2x + -1x2 + 8y 3k + y2 = -2x + -1x2 + 8y Add '-1y2' to each side of the equation. 3k + y2 + -1y2 = -2x + -1x2 + 8y + -1y2 Combine like terms: y2 + -1y2 = 0 3k + 0 = -2x + -1x2 + 8y + -1y2 3k = -2x + -1x2 + 8y + -1y2 Divide each side by '3'. k = -0.6666666667x + -0.3333333333x2 + 2.666666667y + -0.3333333333y2 Simplifying k = -0.6666666667x + -0.3333333333x2 + 2.666666667y + -0.3333333333y2
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