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Simplifying 4.9t2 + 25t + -15 = 0 Reorder the terms: -15 + 25t + 4.9t2 = 0 Solving -15 + 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'. -3.06122449 + 5.102040816t + t2 = 0 Move the constant term to the right: Add '3.06122449' to each side of the equation. -3.06122449 + 5.102040816t + 3.06122449 + t2 = 0 + 3.06122449 Reorder the terms: -3.06122449 + 3.06122449 + 5.102040816t + t2 = 0 + 3.06122449 Combine like terms: -3.06122449 + 3.06122449 = 0.00000000 0.00000000 + 5.102040816t + t2 = 0 + 3.06122449 5.102040816t + t2 = 0 + 3.06122449 Combine like terms: 0 + 3.06122449 = 3.06122449 5.102040816t + t2 = 3.06122449 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 = 3.06122449 + 6.507705122 Reorder the terms: 6.507705122 + 5.102040816t + t2 = 3.06122449 + 6.507705122 Combine like terms: 3.06122449 + 6.507705122 = 9.568929612 6.507705122 + 5.102040816t + t2 = 9.568929612 Factor a perfect square on the left side: (t + 2.551020408)(t + 2.551020408) = 9.568929612 Calculate the square root of the right side: 3.093368651 Break this problem into two subproblems by setting (t + 2.551020408) equal to 3.093368651 and -3.093368651.Subproblem 1
t + 2.551020408 = 3.093368651 Simplifying t + 2.551020408 = 3.093368651 Reorder the terms: 2.551020408 + t = 3.093368651 Solving 2.551020408 + t = 3.093368651 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 = 3.093368651 + -2.551020408 Combine like terms: 2.551020408 + -2.551020408 = 0.000000000 0.000000000 + t = 3.093368651 + -2.551020408 t = 3.093368651 + -2.551020408 Combine like terms: 3.093368651 + -2.551020408 = 0.542348243 t = 0.542348243 Simplifying t = 0.542348243Subproblem 2
t + 2.551020408 = -3.093368651 Simplifying t + 2.551020408 = -3.093368651 Reorder the terms: 2.551020408 + t = -3.093368651 Solving 2.551020408 + t = -3.093368651 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 = -3.093368651 + -2.551020408 Combine like terms: 2.551020408 + -2.551020408 = 0.000000000 0.000000000 + t = -3.093368651 + -2.551020408 t = -3.093368651 + -2.551020408 Combine like terms: -3.093368651 + -2.551020408 = -5.644389059 t = -5.644389059 Simplifying t = -5.644389059Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.542348243, -5.644389059}
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