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Simplifying 4a2 + b2 + c2 + -4a + 6b + -4C + 14 = 0 Reorder the terms: 14 + -4C + -4a + 4a2 + 6b + b2 + c2 = 0 Solving 14 + -4C + -4a + 4a2 + 6b + b2 + c2 = 0 Solving for variable 'C'. Move all terms containing C to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -4C + -4a + 4a2 + 6b + b2 + -14 + c2 = 0 + -14 Reorder the terms: 14 + -14 + -4C + -4a + 4a2 + 6b + b2 + c2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -4C + -4a + 4a2 + 6b + b2 + c2 = 0 + -14 -4C + -4a + 4a2 + 6b + b2 + c2 = 0 + -14 Combine like terms: 0 + -14 = -14 -4C + -4a + 4a2 + 6b + b2 + c2 = -14 Add '4a' to each side of the equation. -4C + -4a + 4a2 + 6b + b2 + 4a + c2 = -14 + 4a Reorder the terms: -4C + -4a + 4a + 4a2 + 6b + b2 + c2 = -14 + 4a Combine like terms: -4a + 4a = 0 -4C + 0 + 4a2 + 6b + b2 + c2 = -14 + 4a -4C + 4a2 + 6b + b2 + c2 = -14 + 4a Add '-4a2' to each side of the equation. -4C + 4a2 + 6b + b2 + -4a2 + c2 = -14 + 4a + -4a2 Reorder the terms: -4C + 4a2 + -4a2 + 6b + b2 + c2 = -14 + 4a + -4a2 Combine like terms: 4a2 + -4a2 = 0 -4C + 0 + 6b + b2 + c2 = -14 + 4a + -4a2 -4C + 6b + b2 + c2 = -14 + 4a + -4a2 Add '-6b' to each side of the equation. -4C + 6b + b2 + -6b + c2 = -14 + 4a + -4a2 + -6b Reorder the terms: -4C + 6b + -6b + b2 + c2 = -14 + 4a + -4a2 + -6b Combine like terms: 6b + -6b = 0 -4C + 0 + b2 + c2 = -14 + 4a + -4a2 + -6b -4C + b2 + c2 = -14 + 4a + -4a2 + -6b Add '-1b2' to each side of the equation. -4C + b2 + -1b2 + c2 = -14 + 4a + -4a2 + -6b + -1b2 Combine like terms: b2 + -1b2 = 0 -4C + 0 + c2 = -14 + 4a + -4a2 + -6b + -1b2 -4C + c2 = -14 + 4a + -4a2 + -6b + -1b2 Add '-1c2' to each side of the equation. -4C + c2 + -1c2 = -14 + 4a + -4a2 + -6b + -1b2 + -1c2 Combine like terms: c2 + -1c2 = 0 -4C + 0 = -14 + 4a + -4a2 + -6b + -1b2 + -1c2 -4C = -14 + 4a + -4a2 + -6b + -1b2 + -1c2 Divide each side by '-4'. C = 3.5 + -1a + a2 + 1.5b + 0.25b2 + 0.25c2 Simplifying C = 3.5 + -1a + a2 + 1.5b + 0.25b2 + 0.25c2
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