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Simplifying 4x2 + -17 + 31 = 6x + 3 Reorder the terms: -17 + 31 + 4x2 = 6x + 3 Combine like terms: -17 + 31 = 14 14 + 4x2 = 6x + 3 Reorder the terms: 14 + 4x2 = 3 + 6x Solving 14 + 4x2 = 3 + 6x Solving for variable 'x'. Reorder the terms: 14 + -3 + -6x + 4x2 = 3 + 6x + -3 + -6x Combine like terms: 14 + -3 = 11 11 + -6x + 4x2 = 3 + 6x + -3 + -6x Reorder the terms: 11 + -6x + 4x2 = 3 + -3 + 6x + -6x Combine like terms: 3 + -3 = 0 11 + -6x + 4x2 = 0 + 6x + -6x 11 + -6x + 4x2 = 6x + -6x Combine like terms: 6x + -6x = 0 11 + -6x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2.75 + -1.5x + x2 = 0 Move the constant term to the right: Add '-2.75' to each side of the equation. 2.75 + -1.5x + -2.75 + x2 = 0 + -2.75 Reorder the terms: 2.75 + -2.75 + -1.5x + x2 = 0 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + -1.5x + x2 = 0 + -2.75 -1.5x + x2 = 0 + -2.75 Combine like terms: 0 + -2.75 = -2.75 -1.5x + x2 = -2.75 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 = -2.75 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = -2.75 + 0.5625 Combine like terms: -2.75 + 0.5625 = -2.1875 0.5625 + -1.5x + x2 = -2.1875 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = -2.1875 Can't calculate square root of the right side. The solution to this equation could not be determined.
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