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Simplifying 4x2 + 29x + 90 = 0 Reorder the terms: 90 + 29x + 4x2 = 0 Solving 90 + 29x + 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'. 22.5 + 7.25x + x2 = 0 Move the constant term to the right: Add '-22.5' to each side of the equation. 22.5 + 7.25x + -22.5 + x2 = 0 + -22.5 Reorder the terms: 22.5 + -22.5 + 7.25x + x2 = 0 + -22.5 Combine like terms: 22.5 + -22.5 = 0.0 0.0 + 7.25x + x2 = 0 + -22.5 7.25x + x2 = 0 + -22.5 Combine like terms: 0 + -22.5 = -22.5 7.25x + x2 = -22.5 The x term is 7.25x. Take half its coefficient (3.625). Square it (13.140625) and add it to both sides. Add '13.140625' to each side of the equation. 7.25x + 13.140625 + x2 = -22.5 + 13.140625 Reorder the terms: 13.140625 + 7.25x + x2 = -22.5 + 13.140625 Combine like terms: -22.5 + 13.140625 = -9.359375 13.140625 + 7.25x + x2 = -9.359375 Factor a perfect square on the left side: (x + 3.625)(x + 3.625) = -9.359375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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