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Simplifying t2 + -3.2t + -3.2 = 49 Reorder the terms: -3.2 + -3.2t + t2 = 49 Solving -3.2 + -3.2t + t2 = 49 Solving for variable 't'. Reorder the terms: -3.2 + -49 + -3.2t + t2 = 49 + -49 Combine like terms: -3.2 + -49 = -52.2 -52.2 + -3.2t + t2 = 49 + -49 Combine like terms: 49 + -49 = 0 -52.2 + -3.2t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '52.2' to each side of the equation. -52.2 + -3.2t + 52.2 + t2 = 0 + 52.2 Reorder the terms: -52.2 + 52.2 + -3.2t + t2 = 0 + 52.2 Combine like terms: -52.2 + 52.2 = 0.0 0.0 + -3.2t + t2 = 0 + 52.2 -3.2t + t2 = 0 + 52.2 Combine like terms: 0 + 52.2 = 52.2 -3.2t + t2 = 52.2 The t term is -3.2t. Take half its coefficient (-1.6). Square it (2.56) and add it to both sides. Add '2.56' to each side of the equation. -3.2t + 2.56 + t2 = 52.2 + 2.56 Reorder the terms: 2.56 + -3.2t + t2 = 52.2 + 2.56 Combine like terms: 52.2 + 2.56 = 54.76 2.56 + -3.2t + t2 = 54.76 Factor a perfect square on the left side: (t + -1.6)(t + -1.6) = 54.76 Calculate the square root of the right side: 7.4 Break this problem into two subproblems by setting (t + -1.6) equal to 7.4 and -7.4.Subproblem 1
t + -1.6 = 7.4 Simplifying t + -1.6 = 7.4 Reorder the terms: -1.6 + t = 7.4 Solving -1.6 + t = 7.4 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + t = 7.4 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + t = 7.4 + 1.6 t = 7.4 + 1.6 Combine like terms: 7.4 + 1.6 = 9 t = 9 Simplifying t = 9Subproblem 2
t + -1.6 = -7.4 Simplifying t + -1.6 = -7.4 Reorder the terms: -1.6 + t = -7.4 Solving -1.6 + t = -7.4 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + t = -7.4 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + t = -7.4 + 1.6 t = -7.4 + 1.6 Combine like terms: -7.4 + 1.6 = -5.8 t = -5.8 Simplifying t = -5.8Solution
The solution to the problem is based on the solutions from the subproblems. t = {9, -5.8}
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