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Simplifying 4x = 2x2 + 3 Reorder the terms: 4x = 3 + 2x2 Solving 4x = 3 + 2x2 Solving for variable 'x'. Reorder the terms: -3 + 4x + -2x2 = 3 + 2x2 + -3 + -2x2 Reorder the terms: -3 + 4x + -2x2 = 3 + -3 + 2x2 + -2x2 Combine like terms: 3 + -3 = 0 -3 + 4x + -2x2 = 0 + 2x2 + -2x2 -3 + 4x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -3 + 4x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 1.5 + -2x + x2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -2x + -1.5 + x2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -2x + x2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -2x + x2 = 0 + -1.5 -2x + x2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -2x + x2 = -1.5 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = -1.5 + 1 Reorder the terms: 1 + -2x + x2 = -1.5 + 1 Combine like terms: -1.5 + 1 = -0.5 1 + -2x + x2 = -0.5 Factor a perfect square on the left side: (x + -1)(x + -1) = -0.5 Can't calculate square root of the right side. The solution to this equation could not be determined.
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