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Simplifying 5t2 + 3t = -15 + -9 Reorder the terms: 3t + 5t2 = -15 + -9 Combine like terms: -15 + -9 = -24 3t + 5t2 = -24 Solving 3t + 5t2 = -24 Solving for variable 't'. Reorder the terms: 24 + 3t + 5t2 = -24 + 24 Combine like terms: -24 + 24 = 0 24 + 3t + 5t2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 4.8 + 0.6t + t2 = 0 Move the constant term to the right: Add '-4.8' to each side of the equation. 4.8 + 0.6t + -4.8 + t2 = 0 + -4.8 Reorder the terms: 4.8 + -4.8 + 0.6t + t2 = 0 + -4.8 Combine like terms: 4.8 + -4.8 = 0.0 0.0 + 0.6t + t2 = 0 + -4.8 0.6t + t2 = 0 + -4.8 Combine like terms: 0 + -4.8 = -4.8 0.6t + t2 = -4.8 The t term is 0.6t. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6t + 0.09 + t2 = -4.8 + 0.09 Reorder the terms: 0.09 + 0.6t + t2 = -4.8 + 0.09 Combine like terms: -4.8 + 0.09 = -4.71 0.09 + 0.6t + t2 = -4.71 Factor a perfect square on the left side: (t + 0.3)(t + 0.3) = -4.71 Can't calculate square root of the right side. The solution to this equation could not be determined.
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