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Simplifying 4x2 + 5x + 3 = 2x + 3x2 Reorder the terms: 3 + 5x + 4x2 = 2x + 3x2 Solving 3 + 5x + 4x2 = 2x + 3x2 Solving for variable 'x'. Reorder the terms: 3 + 5x + -2x + 4x2 + -3x2 = 2x + 3x2 + -2x + -3x2 Combine like terms: 5x + -2x = 3x 3 + 3x + 4x2 + -3x2 = 2x + 3x2 + -2x + -3x2 Combine like terms: 4x2 + -3x2 = 1x2 3 + 3x + 1x2 = 2x + 3x2 + -2x + -3x2 Reorder the terms: 3 + 3x + 1x2 = 2x + -2x + 3x2 + -3x2 Combine like terms: 2x + -2x = 0 3 + 3x + 1x2 = 0 + 3x2 + -3x2 3 + 3x + 1x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 3 + 3x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + 3x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + 3x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 3x + x2 = 0 + -3 3x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 3x + x2 = -3 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = -3 + 2.25 Reorder the terms: 2.25 + 3x + x2 = -3 + 2.25 Combine like terms: -3 + 2.25 = -0.75 2.25 + 3x + x2 = -0.75 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = -0.75 Can't calculate square root of the right side. The solution to this equation could not be determined.
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