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Simplifying 3t2 + 3t = 100 Reorder the terms: 3t + 3t2 = 100 Solving 3t + 3t2 = 100 Solving for variable 't'. Reorder the terms: -100 + 3t + 3t2 = 100 + -100 Combine like terms: 100 + -100 = 0 -100 + 3t + 3t2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -33.33333333 + t + t2 = 0 Move the constant term to the right: Add '33.33333333' to each side of the equation. -33.33333333 + t + 33.33333333 + t2 = 0 + 33.33333333 Reorder the terms: -33.33333333 + 33.33333333 + t + t2 = 0 + 33.33333333 Combine like terms: -33.33333333 + 33.33333333 = 0.00000000 0.00000000 + t + t2 = 0 + 33.33333333 t + t2 = 0 + 33.33333333 Combine like terms: 0 + 33.33333333 = 33.33333333 t + t2 = 33.33333333 The t term is t. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + t2 = 33.33333333 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + t2 = 33.33333333 + 0.25 Combine like terms: 33.33333333 + 0.25 = 33.58333333 1.25 + t2 = 33.58333333 Factor a perfect square on the left side: (t + 0.5)(t + 0.5) = 33.58333333 Calculate the square root of the right side: 5.795112883 Break this problem into two subproblems by setting (t + 0.5) equal to 5.795112883 and -5.795112883.Subproblem 1
t + 0.5 = 5.795112883 Simplifying t + 0.5 = 5.795112883 Reorder the terms: 0.5 + t = 5.795112883 Solving 0.5 + t = 5.795112883 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = 5.795112883 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = 5.795112883 + -0.5 t = 5.795112883 + -0.5 Combine like terms: 5.795112883 + -0.5 = 5.295112883 t = 5.295112883 Simplifying t = 5.295112883Subproblem 2
t + 0.5 = -5.795112883 Simplifying t + 0.5 = -5.795112883 Reorder the terms: 0.5 + t = -5.795112883 Solving 0.5 + t = -5.795112883 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = -5.795112883 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = -5.795112883 + -0.5 t = -5.795112883 + -0.5 Combine like terms: -5.795112883 + -0.5 = -6.295112883 t = -6.295112883 Simplifying t = -6.295112883Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.295112883, -6.295112883}
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