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