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Simplifying 61 + -6t + -5t2 = 0 Solving 61 + -6t + -5t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -12.2 + 1.2t + t2 = 0 Move the constant term to the right: Add '12.2' to each side of the equation. -12.2 + 1.2t + 12.2 + t2 = 0 + 12.2 Reorder the terms: -12.2 + 12.2 + 1.2t + t2 = 0 + 12.2 Combine like terms: -12.2 + 12.2 = 0.0 0.0 + 1.2t + t2 = 0 + 12.2 1.2t + t2 = 0 + 12.2 Combine like terms: 0 + 12.2 = 12.2 1.2t + t2 = 12.2 The t term is 1.2t. Take half its coefficient (0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. 1.2t + 0.36 + t2 = 12.2 + 0.36 Reorder the terms: 0.36 + 1.2t + t2 = 12.2 + 0.36 Combine like terms: 12.2 + 0.36 = 12.56 0.36 + 1.2t + t2 = 12.56 Factor a perfect square on the left side: (t + 0.6)(t + 0.6) = 12.56 Calculate the square root of the right side: 3.544009029 Break this problem into two subproblems by setting (t + 0.6) equal to 3.544009029 and -3.544009029.Subproblem 1
t + 0.6 = 3.544009029 Simplifying t + 0.6 = 3.544009029 Reorder the terms: 0.6 + t = 3.544009029 Solving 0.6 + t = 3.544009029 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + t = 3.544009029 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + t = 3.544009029 + -0.6 t = 3.544009029 + -0.6 Combine like terms: 3.544009029 + -0.6 = 2.944009029 t = 2.944009029 Simplifying t = 2.944009029Subproblem 2
t + 0.6 = -3.544009029 Simplifying t + 0.6 = -3.544009029 Reorder the terms: 0.6 + t = -3.544009029 Solving 0.6 + t = -3.544009029 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + t = -3.544009029 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + t = -3.544009029 + -0.6 t = -3.544009029 + -0.6 Combine like terms: -3.544009029 + -0.6 = -4.144009029 t = -4.144009029 Simplifying t = -4.144009029Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.944009029, -4.144009029}
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