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Simplifying 2x2 + 6y2 + 32c + -48y + 212 = 0 Reorder the terms: 212 + 32c + 2x2 + -48y + 6y2 = 0 Solving 212 + 32c + 2x2 + -48y + 6y2 = 0 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-212' to each side of the equation. 212 + 32c + 2x2 + -48y + -212 + 6y2 = 0 + -212 Reorder the terms: 212 + -212 + 32c + 2x2 + -48y + 6y2 = 0 + -212 Combine like terms: 212 + -212 = 0 0 + 32c + 2x2 + -48y + 6y2 = 0 + -212 32c + 2x2 + -48y + 6y2 = 0 + -212 Combine like terms: 0 + -212 = -212 32c + 2x2 + -48y + 6y2 = -212 Add '-2x2' to each side of the equation. 32c + 2x2 + -48y + -2x2 + 6y2 = -212 + -2x2 Reorder the terms: 32c + 2x2 + -2x2 + -48y + 6y2 = -212 + -2x2 Combine like terms: 2x2 + -2x2 = 0 32c + 0 + -48y + 6y2 = -212 + -2x2 32c + -48y + 6y2 = -212 + -2x2 Add '48y' to each side of the equation. 32c + -48y + 48y + 6y2 = -212 + -2x2 + 48y Combine like terms: -48y + 48y = 0 32c + 0 + 6y2 = -212 + -2x2 + 48y 32c + 6y2 = -212 + -2x2 + 48y Add '-6y2' to each side of the equation. 32c + 6y2 + -6y2 = -212 + -2x2 + 48y + -6y2 Combine like terms: 6y2 + -6y2 = 0 32c + 0 = -212 + -2x2 + 48y + -6y2 32c = -212 + -2x2 + 48y + -6y2 Divide each side by '32'. c = -6.625 + -0.0625x2 + 1.5y + -0.1875y2 Simplifying c = -6.625 + -0.0625x2 + 1.5y + -0.1875y2
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