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Simplifying 2x + 3x + 3 + 4x2 + 10 + x = 0 Reorder the terms: 3 + 10 + 2x + 3x + x + 4x2 = 0 Combine like terms: 3 + 10 = 13 13 + 2x + 3x + x + 4x2 = 0 Combine like terms: 2x + 3x = 5x 13 + 5x + x + 4x2 = 0 Combine like terms: 5x + x = 6x 13 + 6x + 4x2 = 0 Solving 13 + 6x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 3.25 + 1.5x + x2 = 0 Move the constant term to the right: Add '-3.25' to each side of the equation. 3.25 + 1.5x + -3.25 + x2 = 0 + -3.25 Reorder the terms: 3.25 + -3.25 + 1.5x + x2 = 0 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + 1.5x + x2 = 0 + -3.25 1.5x + x2 = 0 + -3.25 Combine like terms: 0 + -3.25 = -3.25 1.5x + x2 = -3.25 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = -3.25 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = -3.25 + 0.5625 Combine like terms: -3.25 + 0.5625 = -2.6875 0.5625 + 1.5x + x2 = -2.6875 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = -2.6875 Can't calculate square root of the right side. The solution to this equation could not be determined.
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