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Simplifying 0 = 0.2x2 + -1.3x + 3 Reorder the terms: 0 = 3 + -1.3x + 0.2x2 Solving 0 = 3 + -1.3x + 0.2x2 Solving for variable 'x'. Combine like terms: 0 + -3 = -3 -3 + 1.3x + -0.2x2 = 3 + -1.3x + 0.2x2 + -3 + 1.3x + -0.2x2 Reorder the terms: -3 + 1.3x + -0.2x2 = 3 + -3 + -1.3x + 1.3x + 0.2x2 + -0.2x2 Combine like terms: 3 + -3 = 0 -3 + 1.3x + -0.2x2 = 0 + -1.3x + 1.3x + 0.2x2 + -0.2x2 -3 + 1.3x + -0.2x2 = -1.3x + 1.3x + 0.2x2 + -0.2x2 Combine like terms: -1.3x + 1.3x = 0.0 -3 + 1.3x + -0.2x2 = 0.0 + 0.2x2 + -0.2x2 -3 + 1.3x + -0.2x2 = 0.2x2 + -0.2x2 Combine like terms: 0.2x2 + -0.2x2 = 0.0 -3 + 1.3x + -0.2x2 = 0.0 Begin completing the square. Divide all terms by -0.2 the coefficient of the squared term: Divide each side by '-0.2'. 15 + -6.5x + x2 = 0 Move the constant term to the right: Add '-15' to each side of the equation. 15 + -6.5x + -15 + x2 = 0 + -15 Reorder the terms: 15 + -15 + -6.5x + x2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -6.5x + x2 = 0 + -15 -6.5x + x2 = 0 + -15 Combine like terms: 0 + -15 = -15 -6.5x + x2 = -15 The x term is -6.5x. Take half its coefficient (-3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. -6.5x + 10.5625 + x2 = -15 + 10.5625 Reorder the terms: 10.5625 + -6.5x + x2 = -15 + 10.5625 Combine like terms: -15 + 10.5625 = -4.4375 10.5625 + -6.5x + x2 = -4.4375 Factor a perfect square on the left side: (x + -3.25)(x + -3.25) = -4.4375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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