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Simplifying 1.2t2 = 3.5t + 7 Reorder the terms: 1.2t2 = 7 + 3.5t Solving 1.2t2 = 7 + 3.5t Solving for variable 't'. Reorder the terms: -7 + -3.5t + 1.2t2 = 7 + 3.5t + -7 + -3.5t Reorder the terms: -7 + -3.5t + 1.2t2 = 7 + -7 + 3.5t + -3.5t Combine like terms: 7 + -7 = 0 -7 + -3.5t + 1.2t2 = 0 + 3.5t + -3.5t -7 + -3.5t + 1.2t2 = 3.5t + -3.5t Combine like terms: 3.5t + -3.5t = 0.0 -7 + -3.5t + 1.2t2 = 0.0 Begin completing the square. Divide all terms by 1.2 the coefficient of the squared term: Divide each side by '1.2'. -5.833333333 + -2.916666667t + t2 = 0 Move the constant term to the right: Add '5.833333333' to each side of the equation. -5.833333333 + -2.916666667t + 5.833333333 + t2 = 0 + 5.833333333 Reorder the terms: -5.833333333 + 5.833333333 + -2.916666667t + t2 = 0 + 5.833333333 Combine like terms: -5.833333333 + 5.833333333 = 0.000000000 0.000000000 + -2.916666667t + t2 = 0 + 5.833333333 -2.916666667t + t2 = 0 + 5.833333333 Combine like terms: 0 + 5.833333333 = 5.833333333 -2.916666667t + t2 = 5.833333333 The t term is -2.916666667t. Take half its coefficient (-1.458333334). Square it (2.126736113) and add it to both sides. Add '2.126736113' to each side of the equation. -2.916666667t + 2.126736113 + t2 = 5.833333333 + 2.126736113 Reorder the terms: 2.126736113 + -2.916666667t + t2 = 5.833333333 + 2.126736113 Combine like terms: 5.833333333 + 2.126736113 = 7.960069446 2.126736113 + -2.916666667t + t2 = 7.960069446 Factor a perfect square on the left side: (t + -1.458333334)(t + -1.458333334) = 7.960069446 Calculate the square root of the right side: 2.821359503 Break this problem into two subproblems by setting (t + -1.458333334) equal to 2.821359503 and -2.821359503.Subproblem 1
t + -1.458333334 = 2.821359503 Simplifying t + -1.458333334 = 2.821359503 Reorder the terms: -1.458333334 + t = 2.821359503 Solving -1.458333334 + t = 2.821359503 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.458333334' to each side of the equation. -1.458333334 + 1.458333334 + t = 2.821359503 + 1.458333334 Combine like terms: -1.458333334 + 1.458333334 = 0.000000000 0.000000000 + t = 2.821359503 + 1.458333334 t = 2.821359503 + 1.458333334 Combine like terms: 2.821359503 + 1.458333334 = 4.279692837 t = 4.279692837 Simplifying t = 4.279692837Subproblem 2
t + -1.458333334 = -2.821359503 Simplifying t + -1.458333334 = -2.821359503 Reorder the terms: -1.458333334 + t = -2.821359503 Solving -1.458333334 + t = -2.821359503 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.458333334' to each side of the equation. -1.458333334 + 1.458333334 + t = -2.821359503 + 1.458333334 Combine like terms: -1.458333334 + 1.458333334 = 0.000000000 0.000000000 + t = -2.821359503 + 1.458333334 t = -2.821359503 + 1.458333334 Combine like terms: -2.821359503 + 1.458333334 = -1.363026169 t = -1.363026169 Simplifying t = -1.363026169Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.279692837, -1.363026169}
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