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Simplifying 4x2 + 1 = -3x Reorder the terms: 1 + 4x2 = -3x Solving 1 + 4x2 = -3x Solving for variable 'x'. Reorder the terms: 1 + 3x + 4x2 = -3x + 3x Combine like terms: -3x + 3x = 0 1 + 3x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.25 + 0.75x + x2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + 0.75x + -0.25 + x2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + 0.75x + x2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + 0.75x + x2 = 0 + -0.25 0.75x + x2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 0.75x + x2 = -0.25 The x term is 0.75x. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75x + 0.140625 + x2 = -0.25 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = -0.25 + 0.140625 Combine like terms: -0.25 + 0.140625 = -0.109375 0.140625 + 0.75x + x2 = -0.109375 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = -0.109375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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