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Simplifying 4x2 + -15x + 31 = 6x + -4 Reorder the terms: 31 + -15x + 4x2 = 6x + -4 Reorder the terms: 31 + -15x + 4x2 = -4 + 6x Solving 31 + -15x + 4x2 = -4 + 6x Solving for variable 'x'. Reorder the terms: 31 + 4 + -15x + -6x + 4x2 = -4 + 6x + 4 + -6x Combine like terms: 31 + 4 = 35 35 + -15x + -6x + 4x2 = -4 + 6x + 4 + -6x Combine like terms: -15x + -6x = -21x 35 + -21x + 4x2 = -4 + 6x + 4 + -6x Reorder the terms: 35 + -21x + 4x2 = -4 + 4 + 6x + -6x Combine like terms: -4 + 4 = 0 35 + -21x + 4x2 = 0 + 6x + -6x 35 + -21x + 4x2 = 6x + -6x Combine like terms: 6x + -6x = 0 35 + -21x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 8.75 + -5.25x + x2 = 0 Move the constant term to the right: Add '-8.75' to each side of the equation. 8.75 + -5.25x + -8.75 + x2 = 0 + -8.75 Reorder the terms: 8.75 + -8.75 + -5.25x + x2 = 0 + -8.75 Combine like terms: 8.75 + -8.75 = 0.00 0.00 + -5.25x + x2 = 0 + -8.75 -5.25x + x2 = 0 + -8.75 Combine like terms: 0 + -8.75 = -8.75 -5.25x + x2 = -8.75 The x term is -5.25x. Take half its coefficient (-2.625). Square it (6.890625) and add it to both sides. Add '6.890625' to each side of the equation. -5.25x + 6.890625 + x2 = -8.75 + 6.890625 Reorder the terms: 6.890625 + -5.25x + x2 = -8.75 + 6.890625 Combine like terms: -8.75 + 6.890625 = -1.859375 6.890625 + -5.25x + x2 = -1.859375 Factor a perfect square on the left side: (x + -2.625)(x + -2.625) = -1.859375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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