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Simplifying 4.9t2 + 25t + -10 = 0 Reorder the terms: -10 + 25t + 4.9t2 = 0 Solving -10 + 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'. -2.040816327 + 5.102040816t + t2 = 0 Move the constant term to the right: Add '2.040816327' to each side of the equation. -2.040816327 + 5.102040816t + 2.040816327 + t2 = 0 + 2.040816327 Reorder the terms: -2.040816327 + 2.040816327 + 5.102040816t + t2 = 0 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + 5.102040816t + t2 = 0 + 2.040816327 5.102040816t + t2 = 0 + 2.040816327 Combine like terms: 0 + 2.040816327 = 2.040816327 5.102040816t + t2 = 2.040816327 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 = 2.040816327 + 6.507705122 Reorder the terms: 6.507705122 + 5.102040816t + t2 = 2.040816327 + 6.507705122 Combine like terms: 2.040816327 + 6.507705122 = 8.548521449 6.507705122 + 5.102040816t + t2 = 8.548521449 Factor a perfect square on the left side: (t + 2.551020408)(t + 2.551020408) = 8.548521449 Calculate the square root of the right side: 2.923785466 Break this problem into two subproblems by setting (t + 2.551020408) equal to 2.923785466 and -2.923785466.Subproblem 1
t + 2.551020408 = 2.923785466 Simplifying t + 2.551020408 = 2.923785466 Reorder the terms: 2.551020408 + t = 2.923785466 Solving 2.551020408 + t = 2.923785466 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 = 2.923785466 + -2.551020408 Combine like terms: 2.551020408 + -2.551020408 = 0.000000000 0.000000000 + t = 2.923785466 + -2.551020408 t = 2.923785466 + -2.551020408 Combine like terms: 2.923785466 + -2.551020408 = 0.372765058 t = 0.372765058 Simplifying t = 0.372765058Subproblem 2
t + 2.551020408 = -2.923785466 Simplifying t + 2.551020408 = -2.923785466 Reorder the terms: 2.551020408 + t = -2.923785466 Solving 2.551020408 + t = -2.923785466 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 = -2.923785466 + -2.551020408 Combine like terms: 2.551020408 + -2.551020408 = 0.000000000 0.000000000 + t = -2.923785466 + -2.551020408 t = -2.923785466 + -2.551020408 Combine like terms: -2.923785466 + -2.551020408 = -5.474805874 t = -5.474805874 Simplifying t = -5.474805874Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.372765058, -5.474805874}
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