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Simplifying 0 = 2x2 + -3x + 75 Reorder the terms: 0 = 75 + -3x + 2x2 Solving 0 = 75 + -3x + 2x2 Solving for variable 'x'. Combine like terms: 0 + -75 = -75 -75 + 3x + -2x2 = 75 + -3x + 2x2 + -75 + 3x + -2x2 Reorder the terms: -75 + 3x + -2x2 = 75 + -75 + -3x + 3x + 2x2 + -2x2 Combine like terms: 75 + -75 = 0 -75 + 3x + -2x2 = 0 + -3x + 3x + 2x2 + -2x2 -75 + 3x + -2x2 = -3x + 3x + 2x2 + -2x2 Combine like terms: -3x + 3x = 0 -75 + 3x + -2x2 = 0 + 2x2 + -2x2 -75 + 3x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -75 + 3x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 37.5 + -1.5x + x2 = 0 Move the constant term to the right: Add '-37.5' to each side of the equation. 37.5 + -1.5x + -37.5 + x2 = 0 + -37.5 Reorder the terms: 37.5 + -37.5 + -1.5x + x2 = 0 + -37.5 Combine like terms: 37.5 + -37.5 = 0.0 0.0 + -1.5x + x2 = 0 + -37.5 -1.5x + x2 = 0 + -37.5 Combine like terms: 0 + -37.5 = -37.5 -1.5x + x2 = -37.5 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 = -37.5 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = -37.5 + 0.5625 Combine like terms: -37.5 + 0.5625 = -36.9375 0.5625 + -1.5x + x2 = -36.9375 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = -36.9375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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