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Simplifying 4.9t2 + 25t + 11 = 0 Reorder the terms: 11 + 25t + 4.9t2 = 0 Solving 11 + 25t + 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'. 2.244897959 + 5.102040816t + t2 = 0 Move the constant term to the right: Add '-2.244897959' to each side of the equation. 2.244897959 + 5.102040816t + -2.244897959 + t2 = 0 + -2.244897959 Reorder the terms: 2.244897959 + -2.244897959 + 5.102040816t + t2 = 0 + -2.244897959 Combine like terms: 2.244897959 + -2.244897959 = 0.000000000 0.000000000 + 5.102040816t + t2 = 0 + -2.244897959 5.102040816t + t2 = 0 + -2.244897959 Combine like terms: 0 + -2.244897959 = -2.244897959 5.102040816t + t2 = -2.244897959 The t term is 5.102040816t. Take half its coefficient (2.551020408). Square it (6.507705122) and add it to both sides. Add '6.507705122' to each side of the equation. 5.102040816t + 6.507705122 + t2 = -2.244897959 + 6.507705122 Reorder the terms: 6.507705122 + 5.102040816t + t2 = -2.244897959 + 6.507705122 Combine like terms: -2.244897959 + 6.507705122 = 4.262807163 6.507705122 + 5.102040816t + t2 = 4.262807163 Factor a perfect square on the left side: (t + 2.551020408)(t + 2.551020408) = 4.262807163 Calculate the square root of the right side: 2.06465667 Break this problem into two subproblems by setting (t + 2.551020408) equal to 2.06465667 and -2.06465667.Subproblem 1
t + 2.551020408 = 2.06465667 Simplifying t + 2.551020408 = 2.06465667 Reorder the terms: 2.551020408 + t = 2.06465667 Solving 2.551020408 + t = 2.06465667 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.551020408' to each side of the equation. 2.551020408 + -2.551020408 + t = 2.06465667 + -2.551020408 Combine like terms: 2.551020408 + -2.551020408 = 0.000000000 0.000000000 + t = 2.06465667 + -2.551020408 t = 2.06465667 + -2.551020408 Combine like terms: 2.06465667 + -2.551020408 = -0.486363738 t = -0.486363738 Simplifying t = -0.486363738Subproblem 2
t + 2.551020408 = -2.06465667 Simplifying t + 2.551020408 = -2.06465667 Reorder the terms: 2.551020408 + t = -2.06465667 Solving 2.551020408 + t = -2.06465667 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.551020408' to each side of the equation. 2.551020408 + -2.551020408 + t = -2.06465667 + -2.551020408 Combine like terms: 2.551020408 + -2.551020408 = 0.000000000 0.000000000 + t = -2.06465667 + -2.551020408 t = -2.06465667 + -2.551020408 Combine like terms: -2.06465667 + -2.551020408 = -4.615677078 t = -4.615677078 Simplifying t = -4.615677078Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.486363738, -4.615677078}
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