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Simplifying 105 = 0.33t2 + 2t Reorder the terms: 105 = 2t + 0.33t2 Solving 105 = 2t + 0.33t2 Solving for variable 't'. Reorder the terms: 105 + -2t + -0.33t2 = 2t + -2t + 0.33t2 + -0.33t2 Combine like terms: 2t + -2t = 0 105 + -2t + -0.33t2 = 0 + 0.33t2 + -0.33t2 105 + -2t + -0.33t2 = 0.33t2 + -0.33t2 Combine like terms: 0.33t2 + -0.33t2 = 0.00 105 + -2t + -0.33t2 = 0.00 Begin completing the square. Divide all terms by -0.33 the coefficient of the squared term: Divide each side by '-0.33'. -318.1818182 + 6.060606061t + t2 = 0 Move the constant term to the right: Add '318.1818182' to each side of the equation. -318.1818182 + 6.060606061t + 318.1818182 + t2 = 0 + 318.1818182 Reorder the terms: -318.1818182 + 318.1818182 + 6.060606061t + t2 = 0 + 318.1818182 Combine like terms: -318.1818182 + 318.1818182 = 0.0000000 0.0000000 + 6.060606061t + t2 = 0 + 318.1818182 6.060606061t + t2 = 0 + 318.1818182 Combine like terms: 0 + 318.1818182 = 318.1818182 6.060606061t + t2 = 318.1818182 The t term is 6.060606061t. Take half its coefficient (3.030303031). Square it (9.182736460) and add it to both sides. Add '9.182736460' to each side of the equation. 6.060606061t + 9.182736460 + t2 = 318.1818182 + 9.182736460 Reorder the terms: 9.182736460 + 6.060606061t + t2 = 318.1818182 + 9.182736460 Combine like terms: 318.1818182 + 9.182736460 = 327.36455466 9.182736460 + 6.060606061t + t2 = 327.36455466 Factor a perfect square on the left side: (t + 3.030303031)(t + 3.030303031) = 327.36455466 Calculate the square root of the right side: 18.093218472 Break this problem into two subproblems by setting (t + 3.030303031) equal to 18.093218472 and -18.093218472.Subproblem 1
t + 3.030303031 = 18.093218472 Simplifying t + 3.030303031 = 18.093218472 Reorder the terms: 3.030303031 + t = 18.093218472 Solving 3.030303031 + t = 18.093218472 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3.030303031' to each side of the equation. 3.030303031 + -3.030303031 + t = 18.093218472 + -3.030303031 Combine like terms: 3.030303031 + -3.030303031 = 0.000000000 0.000000000 + t = 18.093218472 + -3.030303031 t = 18.093218472 + -3.030303031 Combine like terms: 18.093218472 + -3.030303031 = 15.062915441 t = 15.062915441 Simplifying t = 15.062915441Subproblem 2
t + 3.030303031 = -18.093218472 Simplifying t + 3.030303031 = -18.093218472 Reorder the terms: 3.030303031 + t = -18.093218472 Solving 3.030303031 + t = -18.093218472 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3.030303031' to each side of the equation. 3.030303031 + -3.030303031 + t = -18.093218472 + -3.030303031 Combine like terms: 3.030303031 + -3.030303031 = 0.000000000 0.000000000 + t = -18.093218472 + -3.030303031 t = -18.093218472 + -3.030303031 Combine like terms: -18.093218472 + -3.030303031 = -21.123521503 t = -21.123521503 Simplifying t = -21.123521503Solution
The solution to the problem is based on the solutions from the subproblems. t = {15.062915441, -21.123521503}
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