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Simplifying 4x2 + x + 75 = 0 Reorder the terms: 75 + x + 4x2 = 0 Solving 75 + x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 18.75 + 0.25x + x2 = 0 Move the constant term to the right: Add '-18.75' to each side of the equation. 18.75 + 0.25x + -18.75 + x2 = 0 + -18.75 Reorder the terms: 18.75 + -18.75 + 0.25x + x2 = 0 + -18.75 Combine like terms: 18.75 + -18.75 = 0.00 0.00 + 0.25x + x2 = 0 + -18.75 0.25x + x2 = 0 + -18.75 Combine like terms: 0 + -18.75 = -18.75 0.25x + x2 = -18.75 The x term is x. 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. 0.25x + 0.25 + x2 = -18.75 + 0.25 Reorder the terms: 0.25 + 0.25x + x2 = -18.75 + 0.25 Combine like terms: -18.75 + 0.25 = -18.5 0.25 + 0.25x + x2 = -18.5 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -18.5 Can't calculate square root of the right side. The solution to this equation could not be determined.
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