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Simplifying 0 = -2x2 + 3x + -106 Reorder the terms: 0 = -106 + 3x + -2x2 Solving 0 = -106 + 3x + -2x2 Solving for variable 'x'. Combine like terms: 0 + 106 = 106 106 + -3x + 2x2 = -106 + 3x + -2x2 + 106 + -3x + 2x2 Reorder the terms: 106 + -3x + 2x2 = -106 + 106 + 3x + -3x + -2x2 + 2x2 Combine like terms: -106 + 106 = 0 106 + -3x + 2x2 = 0 + 3x + -3x + -2x2 + 2x2 106 + -3x + 2x2 = 3x + -3x + -2x2 + 2x2 Combine like terms: 3x + -3x = 0 106 + -3x + 2x2 = 0 + -2x2 + 2x2 106 + -3x + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 106 + -3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 53 + -1.5x + x2 = 0 Move the constant term to the right: Add '-53' to each side of the equation. 53 + -1.5x + -53 + x2 = 0 + -53 Reorder the terms: 53 + -53 + -1.5x + x2 = 0 + -53 Combine like terms: 53 + -53 = 0 0 + -1.5x + x2 = 0 + -53 -1.5x + x2 = 0 + -53 Combine like terms: 0 + -53 = -53 -1.5x + x2 = -53 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 = -53 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = -53 + 0.5625 Combine like terms: -53 + 0.5625 = -52.4375 0.5625 + -1.5x + x2 = -52.4375 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = -52.4375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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