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Simplifying (4.9t2) + 0.28t + -2.2 = 0 Reorder the terms: -2.2 + 0.28t + (4.9t2) = 0 Solving -2.2 + 0.28t + (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'. -0.4489795918 + 0.05714285714t + t2 = 0 Move the constant term to the right: Add '0.4489795918' to each side of the equation. -0.4489795918 + 0.05714285714t + 0.4489795918 + t2 = 0 + 0.4489795918 Reorder the terms: -0.4489795918 + 0.4489795918 + 0.05714285714t + t2 = 0 + 0.4489795918 Combine like terms: -0.4489795918 + 0.4489795918 = 0.0000000000 0.0000000000 + 0.05714285714t + t2 = 0 + 0.4489795918 0.05714285714t + t2 = 0 + 0.4489795918 Combine like terms: 0 + 0.4489795918 = 0.4489795918 0.05714285714t + t2 = 0.4489795918 The t term is 0.05714285714t. Take half its coefficient (0.02857142857). Square it (0.0008163265305) and add it to both sides. Add '0.0008163265305' to each side of the equation. 0.05714285714t + 0.0008163265305 + t2 = 0.4489795918 + 0.0008163265305 Reorder the terms: 0.0008163265305 + 0.05714285714t + t2 = 0.4489795918 + 0.0008163265305 Combine like terms: 0.4489795918 + 0.0008163265305 = 0.4497959183305 0.0008163265305 + 0.05714285714t + t2 = 0.4497959183305 Factor a perfect square on the left side: ((t) + 0.02857142857)((t) + 0.02857142857) = 0.4497959183305 Calculate the square root of the right side: 0.670668263 Break this problem into two subproblems by setting ((t) + 0.02857142857) equal to 0.670668263 and -0.670668263.Subproblem 1
(t) + 0.02857142857 = 0.670668263 Simplifying (t) + 0.02857142857 = 0.670668263 t + 0.02857142857 = 0.670668263 Reorder the terms: 0.02857142857 + t = 0.670668263 Solving 0.02857142857 + t = 0.670668263 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.02857142857' to each side of the equation. 0.02857142857 + -0.02857142857 + t = 0.670668263 + -0.02857142857 Combine like terms: 0.02857142857 + -0.02857142857 = 0.00000000000 0.00000000000 + t = 0.670668263 + -0.02857142857 t = 0.670668263 + -0.02857142857 Combine like terms: 0.670668263 + -0.02857142857 = 0.64209683443 t = 0.64209683443 Simplifying t = 0.64209683443Subproblem 2
(t) + 0.02857142857 = -0.670668263 Simplifying (t) + 0.02857142857 = -0.670668263 t + 0.02857142857 = -0.670668263 Reorder the terms: 0.02857142857 + t = -0.670668263 Solving 0.02857142857 + t = -0.670668263 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.02857142857' to each side of the equation. 0.02857142857 + -0.02857142857 + t = -0.670668263 + -0.02857142857 Combine like terms: 0.02857142857 + -0.02857142857 = 0.00000000000 0.00000000000 + t = -0.670668263 + -0.02857142857 t = -0.670668263 + -0.02857142857 Combine like terms: -0.670668263 + -0.02857142857 = -0.69923969157 t = -0.69923969157 Simplifying t = -0.69923969157Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.64209683443, -0.69923969157}
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