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Simplifying 4t2 + 5t + 6 = 0 Reorder the terms: 6 + 5t + 4t2 = 0 Solving 6 + 5t + 4t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.5 + 1.25t + t2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + 1.25t + -1.5 + t2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + 1.25t + t2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + 1.25t + t2 = 0 + -1.5 1.25t + t2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 1.25t + t2 = -1.5 The t term is 1.25t. 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. 1.25t + 0.390625 + t2 = -1.5 + 0.390625 Reorder the terms: 0.390625 + 1.25t + t2 = -1.5 + 0.390625 Combine like terms: -1.5 + 0.390625 = -1.109375 0.390625 + 1.25t + t2 = -1.109375 Factor a perfect square on the left side: (t + 0.625)(t + 0.625) = -1.109375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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