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Simplifying 11t2 + 0.5t = 24 Reorder the terms: 0.5t + 11t2 = 24 Solving 0.5t + 11t2 = 24 Solving for variable 't'. Reorder the terms: -24 + 0.5t + 11t2 = 24 + -24 Combine like terms: 24 + -24 = 0 -24 + 0.5t + 11t2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -2.181818182 + 0.04545454545t + t2 = 0 Move the constant term to the right: Add '2.181818182' to each side of the equation. -2.181818182 + 0.04545454545t + 2.181818182 + t2 = 0 + 2.181818182 Reorder the terms: -2.181818182 + 2.181818182 + 0.04545454545t + t2 = 0 + 2.181818182 Combine like terms: -2.181818182 + 2.181818182 = 0.000000000 0.000000000 + 0.04545454545t + t2 = 0 + 2.181818182 0.04545454545t + t2 = 0 + 2.181818182 Combine like terms: 0 + 2.181818182 = 2.181818182 0.04545454545t + t2 = 2.181818182 The t term is 0.04545454545t. Take half its coefficient (0.02272727273). Square it (0.0005165289257) and add it to both sides. Add '0.0005165289257' to each side of the equation. 0.04545454545t + 0.0005165289257 + t2 = 2.181818182 + 0.0005165289257 Reorder the terms: 0.0005165289257 + 0.04545454545t + t2 = 2.181818182 + 0.0005165289257 Combine like terms: 2.181818182 + 0.0005165289257 = 2.1823347109257 0.0005165289257 + 0.04545454545t + t2 = 2.1823347109257 Factor a perfect square on the left side: (t + 0.02272727273)(t + 0.02272727273) = 2.1823347109257 Calculate the square root of the right side: 1.477272727 Break this problem into two subproblems by setting (t + 0.02272727273) equal to 1.477272727 and -1.477272727.Subproblem 1
t + 0.02272727273 = 1.477272727 Simplifying t + 0.02272727273 = 1.477272727 Reorder the terms: 0.02272727273 + t = 1.477272727 Solving 0.02272727273 + t = 1.477272727 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.02272727273' to each side of the equation. 0.02272727273 + -0.02272727273 + t = 1.477272727 + -0.02272727273 Combine like terms: 0.02272727273 + -0.02272727273 = 0.00000000000 0.00000000000 + t = 1.477272727 + -0.02272727273 t = 1.477272727 + -0.02272727273 Combine like terms: 1.477272727 + -0.02272727273 = 1.45454545427 t = 1.45454545427 Simplifying t = 1.45454545427Subproblem 2
t + 0.02272727273 = -1.477272727 Simplifying t + 0.02272727273 = -1.477272727 Reorder the terms: 0.02272727273 + t = -1.477272727 Solving 0.02272727273 + t = -1.477272727 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.02272727273' to each side of the equation. 0.02272727273 + -0.02272727273 + t = -1.477272727 + -0.02272727273 Combine like terms: 0.02272727273 + -0.02272727273 = 0.00000000000 0.00000000000 + t = -1.477272727 + -0.02272727273 t = -1.477272727 + -0.02272727273 Combine like terms: -1.477272727 + -0.02272727273 = -1.49999999973 t = -1.49999999973 Simplifying t = -1.49999999973Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.45454545427, -1.49999999973}
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