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Simplifying 0 = 2x2 + -5x + 12 Reorder the terms: 0 = 12 + -5x + 2x2 Solving 0 = 12 + -5x + 2x2 Solving for variable 'x'. Combine like terms: 0 + -12 = -12 -12 + 5x + -2x2 = 12 + -5x + 2x2 + -12 + 5x + -2x2 Reorder the terms: -12 + 5x + -2x2 = 12 + -12 + -5x + 5x + 2x2 + -2x2 Combine like terms: 12 + -12 = 0 -12 + 5x + -2x2 = 0 + -5x + 5x + 2x2 + -2x2 -12 + 5x + -2x2 = -5x + 5x + 2x2 + -2x2 Combine like terms: -5x + 5x = 0 -12 + 5x + -2x2 = 0 + 2x2 + -2x2 -12 + 5x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -12 + 5x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 6 + -2.5x + x2 = 0 Move the constant term to the right: Add '-6' to each side of the equation. 6 + -2.5x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + -2.5x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -2.5x + x2 = 0 + -6 -2.5x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 -2.5x + x2 = -6 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = -6 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = -6 + 1.5625 Combine like terms: -6 + 1.5625 = -4.4375 1.5625 + -2.5x + x2 = -4.4375 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = -4.4375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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