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Simplifying 4x2 + 5x + 7 = -1 Reorder the terms: 7 + 5x + 4x2 = -1 Solving 7 + 5x + 4x2 = -1 Solving for variable 'x'. Reorder the terms: 7 + 1 + 5x + 4x2 = -1 + 1 Combine like terms: 7 + 1 = 8 8 + 5x + 4x2 = -1 + 1 Combine like terms: -1 + 1 = 0 8 + 5x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2 + 1.25x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + 1.25x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + 1.25x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 1.25x + x2 = 0 + -2 1.25x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 1.25x + x2 = -2 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 = -2 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = -2 + 0.390625 Combine like terms: -2 + 0.390625 = -1.609375 0.390625 + 1.25x + x2 = -1.609375 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = -1.609375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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