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Simplifying 0.024t2 + -0.576t + 2.303 = 0 Reorder the terms: 2.303 + -0.576t + 0.024t2 = 0 Solving 2.303 + -0.576t + 0.024t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 0.024 the coefficient of the squared term: Divide each side by '0.024'. 95.95833333 + -24t + t2 = 0 Move the constant term to the right: Add '-95.95833333' to each side of the equation. 95.95833333 + -24t + -95.95833333 + t2 = 0 + -95.95833333 Reorder the terms: 95.95833333 + -95.95833333 + -24t + t2 = 0 + -95.95833333 Combine like terms: 95.95833333 + -95.95833333 = 0.00000000 0.00000000 + -24t + t2 = 0 + -95.95833333 -24t + t2 = 0 + -95.95833333 Combine like terms: 0 + -95.95833333 = -95.95833333 -24t + t2 = -95.95833333 The t term is -24t. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24t + 144 + t2 = -95.95833333 + 144 Reorder the terms: 144 + -24t + t2 = -95.95833333 + 144 Combine like terms: -95.95833333 + 144 = 48.04166667 144 + -24t + t2 = 48.04166667 Factor a perfect square on the left side: (t + -12)(t + -12) = 48.04166667 Calculate the square root of the right side: 6.931209611 Break this problem into two subproblems by setting (t + -12) equal to 6.931209611 and -6.931209611.Subproblem 1
t + -12 = 6.931209611 Simplifying t + -12 = 6.931209611 Reorder the terms: -12 + t = 6.931209611 Solving -12 + t = 6.931209611 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + t = 6.931209611 + 12 Combine like terms: -12 + 12 = 0 0 + t = 6.931209611 + 12 t = 6.931209611 + 12 Combine like terms: 6.931209611 + 12 = 18.931209611 t = 18.931209611 Simplifying t = 18.931209611Subproblem 2
t + -12 = -6.931209611 Simplifying t + -12 = -6.931209611 Reorder the terms: -12 + t = -6.931209611 Solving -12 + t = -6.931209611 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + t = -6.931209611 + 12 Combine like terms: -12 + 12 = 0 0 + t = -6.931209611 + 12 t = -6.931209611 + 12 Combine like terms: -6.931209611 + 12 = 5.068790389 t = 5.068790389 Simplifying t = 5.068790389Solution
The solution to the problem is based on the solutions from the subproblems. t = {18.931209611, 5.068790389}
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