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Simplifying -4.9t2 + 25t + 230 = 0 Reorder the terms: 230 + 25t + -4.9t2 = 0 Solving 230 + 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'. -46.93877551 + -5.102040816t + t2 = 0 Move the constant term to the right: Add '46.93877551' to each side of the equation. -46.93877551 + -5.102040816t + 46.93877551 + t2 = 0 + 46.93877551 Reorder the terms: -46.93877551 + 46.93877551 + -5.102040816t + t2 = 0 + 46.93877551 Combine like terms: -46.93877551 + 46.93877551 = 0.00000000 0.00000000 + -5.102040816t + t2 = 0 + 46.93877551 -5.102040816t + t2 = 0 + 46.93877551 Combine like terms: 0 + 46.93877551 = 46.93877551 -5.102040816t + t2 = 46.93877551 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 = 46.93877551 + 6.507705122 Reorder the terms: 6.507705122 + -5.102040816t + t2 = 46.93877551 + 6.507705122 Combine like terms: 46.93877551 + 6.507705122 = 53.446480632 6.507705122 + -5.102040816t + t2 = 53.446480632 Factor a perfect square on the left side: (t + -2.551020408)(t + -2.551020408) = 53.446480632 Calculate the square root of the right side: 7.310709995 Break this problem into two subproblems by setting (t + -2.551020408) equal to 7.310709995 and -7.310709995.Subproblem 1
t + -2.551020408 = 7.310709995 Simplifying t + -2.551020408 = 7.310709995 Reorder the terms: -2.551020408 + t = 7.310709995 Solving -2.551020408 + t = 7.310709995 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 = 7.310709995 + 2.551020408 Combine like terms: -2.551020408 + 2.551020408 = 0.000000000 0.000000000 + t = 7.310709995 + 2.551020408 t = 7.310709995 + 2.551020408 Combine like terms: 7.310709995 + 2.551020408 = 9.861730403 t = 9.861730403 Simplifying t = 9.861730403Subproblem 2
t + -2.551020408 = -7.310709995 Simplifying t + -2.551020408 = -7.310709995 Reorder the terms: -2.551020408 + t = -7.310709995 Solving -2.551020408 + t = -7.310709995 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 = -7.310709995 + 2.551020408 Combine like terms: -2.551020408 + 2.551020408 = 0.000000000 0.000000000 + t = -7.310709995 + 2.551020408 t = -7.310709995 + 2.551020408 Combine like terms: -7.310709995 + 2.551020408 = -4.759689587 t = -4.759689587 Simplifying t = -4.759689587Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.861730403, -4.759689587}
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