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Simplifying 4x2 + -2x + 7 = 5 + -3x Reorder the terms: 7 + -2x + 4x2 = 5 + -3x Solving 7 + -2x + 4x2 = 5 + -3x Solving for variable 'x'. Reorder the terms: 7 + -5 + -2x + 3x + 4x2 = 5 + -3x + -5 + 3x Combine like terms: 7 + -5 = 2 2 + -2x + 3x + 4x2 = 5 + -3x + -5 + 3x Combine like terms: -2x + 3x = 1x 2 + 1x + 4x2 = 5 + -3x + -5 + 3x Reorder the terms: 2 + 1x + 4x2 = 5 + -5 + -3x + 3x Combine like terms: 5 + -5 = 0 2 + 1x + 4x2 = 0 + -3x + 3x 2 + 1x + 4x2 = -3x + 3x Combine like terms: -3x + 3x = 0 2 + 1x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.5 + 0.25x + x2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + 0.25x + -0.5 + x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + 0.25x + x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + 0.25x + x2 = 0 + -0.5 0.25x + x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 0.25x + x2 = -0.5 The x term is 0.25x. Take half its coefficient (0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. 0.25x + 0.015625 + x2 = -0.5 + 0.015625 Reorder the terms: 0.015625 + 0.25x + x2 = -0.5 + 0.015625 Combine like terms: -0.5 + 0.015625 = -0.484375 0.015625 + 0.25x + x2 = -0.484375 Factor a perfect square on the left side: (x + 0.125)(x + 0.125) = -0.484375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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