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Simplifying 19 = -3.5x2 + 14x + 3 Reorder the terms: 19 = 3 + 14x + -3.5x2 Solving 19 = 3 + 14x + -3.5x2 Solving for variable 'x'. Combine like terms: 19 + -3 = 16 16 + -14x + 3.5x2 = 3 + 14x + -3.5x2 + -3 + -14x + 3.5x2 Reorder the terms: 16 + -14x + 3.5x2 = 3 + -3 + 14x + -14x + -3.5x2 + 3.5x2 Combine like terms: 3 + -3 = 0 16 + -14x + 3.5x2 = 0 + 14x + -14x + -3.5x2 + 3.5x2 16 + -14x + 3.5x2 = 14x + -14x + -3.5x2 + 3.5x2 Combine like terms: 14x + -14x = 0 16 + -14x + 3.5x2 = 0 + -3.5x2 + 3.5x2 16 + -14x + 3.5x2 = -3.5x2 + 3.5x2 Combine like terms: -3.5x2 + 3.5x2 = 0.0 16 + -14x + 3.5x2 = 0.0 Begin completing the square. Divide all terms by 3.5 the coefficient of the squared term: Divide each side by '3.5'. 4.571428571 + -4x + x2 = 0 Move the constant term to the right: Add '-4.571428571' to each side of the equation. 4.571428571 + -4x + -4.571428571 + x2 = 0 + -4.571428571 Reorder the terms: 4.571428571 + -4.571428571 + -4x + x2 = 0 + -4.571428571 Combine like terms: 4.571428571 + -4.571428571 = 0.000000000 0.000000000 + -4x + x2 = 0 + -4.571428571 -4x + x2 = 0 + -4.571428571 Combine like terms: 0 + -4.571428571 = -4.571428571 -4x + x2 = -4.571428571 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = -4.571428571 + 4 Reorder the terms: 4 + -4x + x2 = -4.571428571 + 4 Combine like terms: -4.571428571 + 4 = -0.571428571 4 + -4x + x2 = -0.571428571 Factor a perfect square on the left side: (x + -2)(x + -2) = -0.571428571 Can't calculate square root of the right side. The solution to this equation could not be determined.
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