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Simplifying 60 = 7t + 4.9t2 Solving 60 = 7t + 4.9t2 Solving for variable 't'. Reorder the terms: 60 + -7t + -4.9t2 = 7t + -7t + 4.9t2 + -4.9t2 Combine like terms: 7t + -7t = 0 60 + -7t + -4.9t2 = 0 + 4.9t2 + -4.9t2 60 + -7t + -4.9t2 = 4.9t2 + -4.9t2 Combine like terms: 4.9t2 + -4.9t2 = 0.0 60 + -7t + -4.9t2 = 0.0 Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -12.24489796 + 1.428571429t + t2 = 0 Move the constant term to the right: Add '12.24489796' to each side of the equation. -12.24489796 + 1.428571429t + 12.24489796 + t2 = 0 + 12.24489796 Reorder the terms: -12.24489796 + 12.24489796 + 1.428571429t + t2 = 0 + 12.24489796 Combine like terms: -12.24489796 + 12.24489796 = 0.00000000 0.00000000 + 1.428571429t + t2 = 0 + 12.24489796 1.428571429t + t2 = 0 + 12.24489796 Combine like terms: 0 + 12.24489796 = 12.24489796 1.428571429t + t2 = 12.24489796 The t term is 1.428571429t. Take half its coefficient (0.7142857145). Square it (0.5102040819) and add it to both sides. Add '0.5102040819' to each side of the equation. 1.428571429t + 0.5102040819 + t2 = 12.24489796 + 0.5102040819 Reorder the terms: 0.5102040819 + 1.428571429t + t2 = 12.24489796 + 0.5102040819 Combine like terms: 12.24489796 + 0.5102040819 = 12.7551020419 0.5102040819 + 1.428571429t + t2 = 12.7551020419 Factor a perfect square on the left side: (t + 0.7142857145)(t + 0.7142857145) = 12.7551020419 Calculate the square root of the right side: 3.571428572 Break this problem into two subproblems by setting (t + 0.7142857145) equal to 3.571428572 and -3.571428572.Subproblem 1
t + 0.7142857145 = 3.571428572 Simplifying t + 0.7142857145 = 3.571428572 Reorder the terms: 0.7142857145 + t = 3.571428572 Solving 0.7142857145 + t = 3.571428572 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.7142857145' to each side of the equation. 0.7142857145 + -0.7142857145 + t = 3.571428572 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + t = 3.571428572 + -0.7142857145 t = 3.571428572 + -0.7142857145 Combine like terms: 3.571428572 + -0.7142857145 = 2.8571428575 t = 2.8571428575 Simplifying t = 2.8571428575Subproblem 2
t + 0.7142857145 = -3.571428572 Simplifying t + 0.7142857145 = -3.571428572 Reorder the terms: 0.7142857145 + t = -3.571428572 Solving 0.7142857145 + t = -3.571428572 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.7142857145' to each side of the equation. 0.7142857145 + -0.7142857145 + t = -3.571428572 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + t = -3.571428572 + -0.7142857145 t = -3.571428572 + -0.7142857145 Combine like terms: -3.571428572 + -0.7142857145 = -4.2857142865 t = -4.2857142865 Simplifying t = -4.2857142865Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.8571428575, -4.2857142865}
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