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Simplifying 4x2 + 5x + 53 = 0 Reorder the terms: 53 + 5x + 4x2 = 0 Solving 53 + 5x + 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'. 13.25 + 1.25x + x2 = 0 Move the constant term to the right: Add '-13.25' to each side of the equation. 13.25 + 1.25x + -13.25 + x2 = 0 + -13.25 Reorder the terms: 13.25 + -13.25 + 1.25x + x2 = 0 + -13.25 Combine like terms: 13.25 + -13.25 = 0.00 0.00 + 1.25x + x2 = 0 + -13.25 1.25x + x2 = 0 + -13.25 Combine like terms: 0 + -13.25 = -13.25 1.25x + x2 = -13.25 The x term is 1.25x. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25x + 0.390625 + x2 = -13.25 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = -13.25 + 0.390625 Combine like terms: -13.25 + 0.390625 = -12.859375 0.390625 + 1.25x + x2 = -12.859375 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = -12.859375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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