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Simplifying 3x + -5 = 2x2 + -6x + 7 Reorder the terms: -5 + 3x = 2x2 + -6x + 7 Reorder the terms: -5 + 3x = 7 + -6x + 2x2 Solving -5 + 3x = 7 + -6x + 2x2 Solving for variable 'x'. Reorder the terms: -5 + -7 + 3x + 6x + -2x2 = 7 + -6x + 2x2 + -7 + 6x + -2x2 Combine like terms: -5 + -7 = -12 -12 + 3x + 6x + -2x2 = 7 + -6x + 2x2 + -7 + 6x + -2x2 Combine like terms: 3x + 6x = 9x -12 + 9x + -2x2 = 7 + -6x + 2x2 + -7 + 6x + -2x2 Reorder the terms: -12 + 9x + -2x2 = 7 + -7 + -6x + 6x + 2x2 + -2x2 Combine like terms: 7 + -7 = 0 -12 + 9x + -2x2 = 0 + -6x + 6x + 2x2 + -2x2 -12 + 9x + -2x2 = -6x + 6x + 2x2 + -2x2 Combine like terms: -6x + 6x = 0 -12 + 9x + -2x2 = 0 + 2x2 + -2x2 -12 + 9x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -12 + 9x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 6 + -4.5x + x2 = 0 Move the constant term to the right: Add '-6' to each side of the equation. 6 + -4.5x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + -4.5x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -4.5x + x2 = 0 + -6 -4.5x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 -4.5x + x2 = -6 The x term is -4.5x. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5x + 5.0625 + x2 = -6 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = -6 + 5.0625 Combine like terms: -6 + 5.0625 = -0.9375 5.0625 + -4.5x + x2 = -0.9375 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = -0.9375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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