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Simplifying 3x2 + -1x + 5 = x2 + 3x + -14 Reorder the terms: 5 + -1x + 3x2 = x2 + 3x + -14 Reorder the terms: 5 + -1x + 3x2 = -14 + 3x + x2 Solving 5 + -1x + 3x2 = -14 + 3x + x2 Solving for variable 'x'. Reorder the terms: 5 + 14 + -1x + -3x + 3x2 + -1x2 = -14 + 3x + x2 + 14 + -3x + -1x2 Combine like terms: 5 + 14 = 19 19 + -1x + -3x + 3x2 + -1x2 = -14 + 3x + x2 + 14 + -3x + -1x2 Combine like terms: -1x + -3x = -4x 19 + -4x + 3x2 + -1x2 = -14 + 3x + x2 + 14 + -3x + -1x2 Combine like terms: 3x2 + -1x2 = 2x2 19 + -4x + 2x2 = -14 + 3x + x2 + 14 + -3x + -1x2 Reorder the terms: 19 + -4x + 2x2 = -14 + 14 + 3x + -3x + x2 + -1x2 Combine like terms: -14 + 14 = 0 19 + -4x + 2x2 = 0 + 3x + -3x + x2 + -1x2 19 + -4x + 2x2 = 3x + -3x + x2 + -1x2 Combine like terms: 3x + -3x = 0 19 + -4x + 2x2 = 0 + x2 + -1x2 19 + -4x + 2x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 19 + -4x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 9.5 + -2x + x2 = 0 Move the constant term to the right: Add '-9.5' to each side of the equation. 9.5 + -2x + -9.5 + x2 = 0 + -9.5 Reorder the terms: 9.5 + -9.5 + -2x + x2 = 0 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + -2x + x2 = 0 + -9.5 -2x + x2 = 0 + -9.5 Combine like terms: 0 + -9.5 = -9.5 -2x + x2 = -9.5 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = -9.5 + 1 Reorder the terms: 1 + -2x + x2 = -9.5 + 1 Combine like terms: -9.5 + 1 = -8.5 1 + -2x + x2 = -8.5 Factor a perfect square on the left side: (x + -1)(x + -1) = -8.5 Can't calculate square root of the right side. The solution to this equation could not be determined.
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