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Simplifying 2X2 + 16X + 33 = X + 3 + X + 3 Reorder the terms: 33 + 16X + 2X2 = X + 3 + X + 3 Reorder the terms: 33 + 16X + 2X2 = 3 + 3 + X + X Combine like terms: 3 + 3 = 6 33 + 16X + 2X2 = 6 + X + X Combine like terms: X + X = 2X 33 + 16X + 2X2 = 6 + 2X Solving 33 + 16X + 2X2 = 6 + 2X Solving for variable 'X'. Reorder the terms: 33 + -6 + 16X + -2X + 2X2 = 6 + 2X + -6 + -2X Combine like terms: 33 + -6 = 27 27 + 16X + -2X + 2X2 = 6 + 2X + -6 + -2X Combine like terms: 16X + -2X = 14X 27 + 14X + 2X2 = 6 + 2X + -6 + -2X Reorder the terms: 27 + 14X + 2X2 = 6 + -6 + 2X + -2X Combine like terms: 6 + -6 = 0 27 + 14X + 2X2 = 0 + 2X + -2X 27 + 14X + 2X2 = 2X + -2X Combine like terms: 2X + -2X = 0 27 + 14X + 2X2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 13.5 + 7X + X2 = 0 Move the constant term to the right: Add '-13.5' to each side of the equation. 13.5 + 7X + -13.5 + X2 = 0 + -13.5 Reorder the terms: 13.5 + -13.5 + 7X + X2 = 0 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + 7X + X2 = 0 + -13.5 7X + X2 = 0 + -13.5 Combine like terms: 0 + -13.5 = -13.5 7X + X2 = -13.5 The X term is 7X. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7X + 12.25 + X2 = -13.5 + 12.25 Reorder the terms: 12.25 + 7X + X2 = -13.5 + 12.25 Combine like terms: -13.5 + 12.25 = -1.25 12.25 + 7X + X2 = -1.25 Factor a perfect square on the left side: (X + 3.5)(X + 3.5) = -1.25 Can't calculate square root of the right side. The solution to this equation could not be determined.
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