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Simplifying (x + 2) = 2x2 + -4x + 19 Reorder the terms: (2 + x) = 2x2 + -4x + 19 Remove parenthesis around (2 + x) 2 + x = 2x2 + -4x + 19 Reorder the terms: 2 + x = 19 + -4x + 2x2 Solving 2 + x = 19 + -4x + 2x2 Solving for variable 'x'. Reorder the terms: 2 + -19 + x + 4x + -2x2 = 19 + -4x + 2x2 + -19 + 4x + -2x2 Combine like terms: 2 + -19 = -17 -17 + x + 4x + -2x2 = 19 + -4x + 2x2 + -19 + 4x + -2x2 Combine like terms: x + 4x = 5x -17 + 5x + -2x2 = 19 + -4x + 2x2 + -19 + 4x + -2x2 Reorder the terms: -17 + 5x + -2x2 = 19 + -19 + -4x + 4x + 2x2 + -2x2 Combine like terms: 19 + -19 = 0 -17 + 5x + -2x2 = 0 + -4x + 4x + 2x2 + -2x2 -17 + 5x + -2x2 = -4x + 4x + 2x2 + -2x2 Combine like terms: -4x + 4x = 0 -17 + 5x + -2x2 = 0 + 2x2 + -2x2 -17 + 5x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -17 + 5x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 8.5 + -2.5x + x2 = 0 Move the constant term to the right: Add '-8.5' to each side of the equation. 8.5 + -2.5x + -8.5 + x2 = 0 + -8.5 Reorder the terms: 8.5 + -8.5 + -2.5x + x2 = 0 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + -2.5x + x2 = 0 + -8.5 -2.5x + x2 = 0 + -8.5 Combine like terms: 0 + -8.5 = -8.5 -2.5x + x2 = -8.5 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 = -8.5 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = -8.5 + 1.5625 Combine like terms: -8.5 + 1.5625 = -6.9375 1.5625 + -2.5x + x2 = -6.9375 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = -6.9375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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