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Simplifying 4.9t2 + -22t + 5 = 0 Reorder the terms: 5 + -22t + 4.9t2 = 0 Solving 5 + -22t + 4.9t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. 1.020408163 + -4.489795918t + t2 = 0 Move the constant term to the right: Add '-1.020408163' to each side of the equation. 1.020408163 + -4.489795918t + -1.020408163 + t2 = 0 + -1.020408163 Reorder the terms: 1.020408163 + -1.020408163 + -4.489795918t + t2 = 0 + -1.020408163 Combine like terms: 1.020408163 + -1.020408163 = 0.000000000 0.000000000 + -4.489795918t + t2 = 0 + -1.020408163 -4.489795918t + t2 = 0 + -1.020408163 Combine like terms: 0 + -1.020408163 = -1.020408163 -4.489795918t + t2 = -1.020408163 The t term is -4.489795918t. Take half its coefficient (-2.244897959). Square it (5.039566846) and add it to both sides. Add '5.039566846' to each side of the equation. -4.489795918t + 5.039566846 + t2 = -1.020408163 + 5.039566846 Reorder the terms: 5.039566846 + -4.489795918t + t2 = -1.020408163 + 5.039566846 Combine like terms: -1.020408163 + 5.039566846 = 4.019158683 5.039566846 + -4.489795918t + t2 = 4.019158683 Factor a perfect square on the left side: (t + -2.244897959)(t + -2.244897959) = 4.019158683 Calculate the square root of the right side: 2.004783949 Break this problem into two subproblems by setting (t + -2.244897959) equal to 2.004783949 and -2.004783949.Subproblem 1
t + -2.244897959 = 2.004783949 Simplifying t + -2.244897959 = 2.004783949 Reorder the terms: -2.244897959 + t = 2.004783949 Solving -2.244897959 + t = 2.004783949 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.244897959' to each side of the equation. -2.244897959 + 2.244897959 + t = 2.004783949 + 2.244897959 Combine like terms: -2.244897959 + 2.244897959 = 0.000000000 0.000000000 + t = 2.004783949 + 2.244897959 t = 2.004783949 + 2.244897959 Combine like terms: 2.004783949 + 2.244897959 = 4.249681908 t = 4.249681908 Simplifying t = 4.249681908Subproblem 2
t + -2.244897959 = -2.004783949 Simplifying t + -2.244897959 = -2.004783949 Reorder the terms: -2.244897959 + t = -2.004783949 Solving -2.244897959 + t = -2.004783949 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.244897959' to each side of the equation. -2.244897959 + 2.244897959 + t = -2.004783949 + 2.244897959 Combine like terms: -2.244897959 + 2.244897959 = 0.000000000 0.000000000 + t = -2.004783949 + 2.244897959 t = -2.004783949 + 2.244897959 Combine like terms: -2.004783949 + 2.244897959 = 0.24011401 t = 0.24011401 Simplifying t = 0.24011401Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.249681908, 0.24011401}
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