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Simplifying 3x2 + 5 = x2 + 2x Reorder the terms: 5 + 3x2 = x2 + 2x Reorder the terms: 5 + 3x2 = 2x + x2 Solving 5 + 3x2 = 2x + x2 Solving for variable 'x'. Reorder the terms: 5 + -2x + 3x2 + -1x2 = 2x + x2 + -2x + -1x2 Combine like terms: 3x2 + -1x2 = 2x2 5 + -2x + 2x2 = 2x + x2 + -2x + -1x2 Reorder the terms: 5 + -2x + 2x2 = 2x + -2x + x2 + -1x2 Combine like terms: 2x + -2x = 0 5 + -2x + 2x2 = 0 + x2 + -1x2 5 + -2x + 2x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 5 + -2x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2.5 + -1x + x2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + -1x + -2.5 + x2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + -1x + x2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + -1x + x2 = 0 + -2.5 -1x + x2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 -1x + x2 = -2.5 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 = -2.5 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -2.5 + 0.25 Combine like terms: -2.5 + 0.25 = -2.25 0.25 + -1x + x2 = -2.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = -2.25 Can't calculate square root of the right side. The solution to this equation could not be determined.
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