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Simplifying 0 = 2x2 + -4x + 9 Reorder the terms: 0 = 9 + -4x + 2x2 Solving 0 = 9 + -4x + 2x2 Solving for variable 'x'. Combine like terms: 0 + -9 = -9 -9 + 4x + -2x2 = 9 + -4x + 2x2 + -9 + 4x + -2x2 Reorder the terms: -9 + 4x + -2x2 = 9 + -9 + -4x + 4x + 2x2 + -2x2 Combine like terms: 9 + -9 = 0 -9 + 4x + -2x2 = 0 + -4x + 4x + 2x2 + -2x2 -9 + 4x + -2x2 = -4x + 4x + 2x2 + -2x2 Combine like terms: -4x + 4x = 0 -9 + 4x + -2x2 = 0 + 2x2 + -2x2 -9 + 4x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -9 + 4x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 4.5 + -2x + x2 = 0 Move the constant term to the right: Add '-4.5' to each side of the equation. 4.5 + -2x + -4.5 + x2 = 0 + -4.5 Reorder the terms: 4.5 + -4.5 + -2x + x2 = 0 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + -2x + x2 = 0 + -4.5 -2x + x2 = 0 + -4.5 Combine like terms: 0 + -4.5 = -4.5 -2x + x2 = -4.5 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = -4.5 + 1 Reorder the terms: 1 + -2x + x2 = -4.5 + 1 Combine like terms: -4.5 + 1 = -3.5 1 + -2x + x2 = -3.5 Factor a perfect square on the left side: (x + -1)(x + -1) = -3.5 Can't calculate square root of the right side. The solution to this equation could not be determined.
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