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Simplifying 4x2 + 5x + 1 = -3 Reorder the terms: 1 + 5x + 4x2 = -3 Solving 1 + 5x + 4x2 = -3 Solving for variable 'x'. Reorder the terms: 1 + 3 + 5x + 4x2 = -3 + 3 Combine like terms: 1 + 3 = 4 4 + 5x + 4x2 = -3 + 3 Combine like terms: -3 + 3 = 0 4 + 5x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1 + 1.25x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 1.25x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 1.25x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 1.25x + x2 = 0 + -1 1.25x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 1.25x + x2 = -1 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 = -1 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = -1 + 0.390625 Combine like terms: -1 + 0.390625 = -0.609375 0.390625 + 1.25x + x2 = -0.609375 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = -0.609375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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