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Simplifying 6t2 + 3t + -25 = 0 Reorder the terms: -25 + 3t + 6t2 = 0 Solving -25 + 3t + 6t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -4.166666667 + 0.5t + t2 = 0 Move the constant term to the right: Add '4.166666667' to each side of the equation. -4.166666667 + 0.5t + 4.166666667 + t2 = 0 + 4.166666667 Reorder the terms: -4.166666667 + 4.166666667 + 0.5t + t2 = 0 + 4.166666667 Combine like terms: -4.166666667 + 4.166666667 = 0.000000000 0.000000000 + 0.5t + t2 = 0 + 4.166666667 0.5t + t2 = 0 + 4.166666667 Combine like terms: 0 + 4.166666667 = 4.166666667 0.5t + t2 = 4.166666667 The t term is 0.5t. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5t + 0.0625 + t2 = 4.166666667 + 0.0625 Reorder the terms: 0.0625 + 0.5t + t2 = 4.166666667 + 0.0625 Combine like terms: 4.166666667 + 0.0625 = 4.229166667 0.0625 + 0.5t + t2 = 4.229166667 Factor a perfect square on the left side: (t + 0.25)(t + 0.25) = 4.229166667 Calculate the square root of the right side: 2.05649378 Break this problem into two subproblems by setting (t + 0.25) equal to 2.05649378 and -2.05649378.Subproblem 1
t + 0.25 = 2.05649378 Simplifying t + 0.25 = 2.05649378 Reorder the terms: 0.25 + t = 2.05649378 Solving 0.25 + t = 2.05649378 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + t = 2.05649378 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + t = 2.05649378 + -0.25 t = 2.05649378 + -0.25 Combine like terms: 2.05649378 + -0.25 = 1.80649378 t = 1.80649378 Simplifying t = 1.80649378Subproblem 2
t + 0.25 = -2.05649378 Simplifying t + 0.25 = -2.05649378 Reorder the terms: 0.25 + t = -2.05649378 Solving 0.25 + t = -2.05649378 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + t = -2.05649378 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + t = -2.05649378 + -0.25 t = -2.05649378 + -0.25 Combine like terms: -2.05649378 + -0.25 = -2.30649378 t = -2.30649378 Simplifying t = -2.30649378Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.80649378, -2.30649378}
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