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Simplifying 0 = (2.20) * t + 4.9t2 + -10 Reorder the terms: 0 = -10 + 2.20t + 4.9t2 Solving 0 = -10 + 2.20t + 4.9t2 Solving for variable 't'. Combine like terms: 0 + 10 = 10 10 + -2.20t + -4.9t2 = -10 + 2.20t + 4.9t2 + 10 + -2.20t + -4.9t2 Reorder the terms: 10 + -2.20t + -4.9t2 = -10 + 10 + 2.20t + -2.20t + 4.9t2 + -4.9t2 Combine like terms: -10 + 10 = 0 10 + -2.20t + -4.9t2 = 0 + 2.20t + -2.20t + 4.9t2 + -4.9t2 10 + -2.20t + -4.9t2 = 2.20t + -2.20t + 4.9t2 + -4.9t2 Combine like terms: 2.20t + -2.20t = 0.00 10 + -2.20t + -4.9t2 = 0.00 + 4.9t2 + -4.9t2 10 + -2.20t + -4.9t2 = 4.9t2 + -4.9t2 Combine like terms: 4.9t2 + -4.9t2 = 0.0 10 + -2.20t + -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'. -2.040816327 + 0.4489795918t + t2 = 0 Move the constant term to the right: Add '2.040816327' to each side of the equation. -2.040816327 + 0.4489795918t + 2.040816327 + t2 = 0 + 2.040816327 Reorder the terms: -2.040816327 + 2.040816327 + 0.4489795918t + t2 = 0 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + 0.4489795918t + t2 = 0 + 2.040816327 0.4489795918t + t2 = 0 + 2.040816327 Combine like terms: 0 + 2.040816327 = 2.040816327 0.4489795918t + t2 = 2.040816327 The t term is 0.4489795918t. Take half its coefficient (0.2244897959). Square it (0.05039566846) and add it to both sides. Add '0.05039566846' to each side of the equation. 0.4489795918t + 0.05039566846 + t2 = 2.040816327 + 0.05039566846 Reorder the terms: 0.05039566846 + 0.4489795918t + t2 = 2.040816327 + 0.05039566846 Combine like terms: 2.040816327 + 0.05039566846 = 2.09121199546 0.05039566846 + 0.4489795918t + t2 = 2.09121199546 Factor a perfect square on the left side: (t + 0.2244897959)(t + 0.2244897959) = 2.09121199546 Calculate the square root of the right side: 1.446102346 Break this problem into two subproblems by setting (t + 0.2244897959) equal to 1.446102346 and -1.446102346.Subproblem 1
t + 0.2244897959 = 1.446102346 Simplifying t + 0.2244897959 = 1.446102346 Reorder the terms: 0.2244897959 + t = 1.446102346 Solving 0.2244897959 + t = 1.446102346 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.2244897959' to each side of the equation. 0.2244897959 + -0.2244897959 + t = 1.446102346 + -0.2244897959 Combine like terms: 0.2244897959 + -0.2244897959 = 0.0000000000 0.0000000000 + t = 1.446102346 + -0.2244897959 t = 1.446102346 + -0.2244897959 Combine like terms: 1.446102346 + -0.2244897959 = 1.2216125501 t = 1.2216125501 Simplifying t = 1.2216125501Subproblem 2
t + 0.2244897959 = -1.446102346 Simplifying t + 0.2244897959 = -1.446102346 Reorder the terms: 0.2244897959 + t = -1.446102346 Solving 0.2244897959 + t = -1.446102346 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.2244897959' to each side of the equation. 0.2244897959 + -0.2244897959 + t = -1.446102346 + -0.2244897959 Combine like terms: 0.2244897959 + -0.2244897959 = 0.0000000000 0.0000000000 + t = -1.446102346 + -0.2244897959 t = -1.446102346 + -0.2244897959 Combine like terms: -1.446102346 + -0.2244897959 = -1.6705921419 t = -1.6705921419 Simplifying t = -1.6705921419Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.2216125501, -1.6705921419}
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