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Simplifying -9.8t2 + 45t + 1 = 0 Reorder the terms: 1 + 45t + -9.8t2 = 0 Solving 1 + 45t + -9.8t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -9.8 the coefficient of the squared term: Divide each side by '-9.8'. -0.1020408163 + -4.591836735t + t2 = 0 Move the constant term to the right: Add '0.1020408163' to each side of the equation. -0.1020408163 + -4.591836735t + 0.1020408163 + t2 = 0 + 0.1020408163 Reorder the terms: -0.1020408163 + 0.1020408163 + -4.591836735t + t2 = 0 + 0.1020408163 Combine like terms: -0.1020408163 + 0.1020408163 = 0.0000000000 0.0000000000 + -4.591836735t + t2 = 0 + 0.1020408163 -4.591836735t + t2 = 0 + 0.1020408163 Combine like terms: 0 + 0.1020408163 = 0.1020408163 -4.591836735t + t2 = 0.1020408163 The t term is -4.591836735t. Take half its coefficient (-2.295918368). Square it (5.271241153) and add it to both sides. Add '5.271241153' to each side of the equation. -4.591836735t + 5.271241153 + t2 = 0.1020408163 + 5.271241153 Reorder the terms: 5.271241153 + -4.591836735t + t2 = 0.1020408163 + 5.271241153 Combine like terms: 0.1020408163 + 5.271241153 = 5.3732819693 5.271241153 + -4.591836735t + t2 = 5.3732819693 Factor a perfect square on the left side: (t + -2.295918368)(t + -2.295918368) = 5.3732819693 Calculate the square root of the right side: 2.318034074 Break this problem into two subproblems by setting (t + -2.295918368) equal to 2.318034074 and -2.318034074.Subproblem 1
t + -2.295918368 = 2.318034074 Simplifying t + -2.295918368 = 2.318034074 Reorder the terms: -2.295918368 + t = 2.318034074 Solving -2.295918368 + t = 2.318034074 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.295918368' to each side of the equation. -2.295918368 + 2.295918368 + t = 2.318034074 + 2.295918368 Combine like terms: -2.295918368 + 2.295918368 = 0.000000000 0.000000000 + t = 2.318034074 + 2.295918368 t = 2.318034074 + 2.295918368 Combine like terms: 2.318034074 + 2.295918368 = 4.613952442 t = 4.613952442 Simplifying t = 4.613952442Subproblem 2
t + -2.295918368 = -2.318034074 Simplifying t + -2.295918368 = -2.318034074 Reorder the terms: -2.295918368 + t = -2.318034074 Solving -2.295918368 + t = -2.318034074 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.295918368' to each side of the equation. -2.295918368 + 2.295918368 + t = -2.318034074 + 2.295918368 Combine like terms: -2.295918368 + 2.295918368 = 0.000000000 0.000000000 + t = -2.318034074 + 2.295918368 t = -2.318034074 + 2.295918368 Combine like terms: -2.318034074 + 2.295918368 = -0.022115706 t = -0.022115706 Simplifying t = -0.022115706Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.613952442, -0.022115706}
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