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Simplifying 4.9t2 + -18t + -32 = 0 Reorder the terms: -32 + -18t + 4.9t2 = 0 Solving -32 + -18t + 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'. -6.530612245 + -3.673469388t + t2 = 0 Move the constant term to the right: Add '6.530612245' to each side of the equation. -6.530612245 + -3.673469388t + 6.530612245 + t2 = 0 + 6.530612245 Reorder the terms: -6.530612245 + 6.530612245 + -3.673469388t + t2 = 0 + 6.530612245 Combine like terms: -6.530612245 + 6.530612245 = 0.000000000 0.000000000 + -3.673469388t + t2 = 0 + 6.530612245 -3.673469388t + t2 = 0 + 6.530612245 Combine like terms: 0 + 6.530612245 = 6.530612245 -3.673469388t + t2 = 6.530612245 The t term is -3.673469388t. Take half its coefficient (-1.836734694). Square it (3.373594336) and add it to both sides. Add '3.373594336' to each side of the equation. -3.673469388t + 3.373594336 + t2 = 6.530612245 + 3.373594336 Reorder the terms: 3.373594336 + -3.673469388t + t2 = 6.530612245 + 3.373594336 Combine like terms: 6.530612245 + 3.373594336 = 9.904206581 3.373594336 + -3.673469388t + t2 = 9.904206581 Factor a perfect square on the left side: (t + -1.836734694)(t + -1.836734694) = 9.904206581 Calculate the square root of the right side: 3.147094943 Break this problem into two subproblems by setting (t + -1.836734694) equal to 3.147094943 and -3.147094943.Subproblem 1
t + -1.836734694 = 3.147094943 Simplifying t + -1.836734694 = 3.147094943 Reorder the terms: -1.836734694 + t = 3.147094943 Solving -1.836734694 + t = 3.147094943 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.836734694' to each side of the equation. -1.836734694 + 1.836734694 + t = 3.147094943 + 1.836734694 Combine like terms: -1.836734694 + 1.836734694 = 0.000000000 0.000000000 + t = 3.147094943 + 1.836734694 t = 3.147094943 + 1.836734694 Combine like terms: 3.147094943 + 1.836734694 = 4.983829637 t = 4.983829637 Simplifying t = 4.983829637Subproblem 2
t + -1.836734694 = -3.147094943 Simplifying t + -1.836734694 = -3.147094943 Reorder the terms: -1.836734694 + t = -3.147094943 Solving -1.836734694 + t = -3.147094943 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.836734694' to each side of the equation. -1.836734694 + 1.836734694 + t = -3.147094943 + 1.836734694 Combine like terms: -1.836734694 + 1.836734694 = 0.000000000 0.000000000 + t = -3.147094943 + 1.836734694 t = -3.147094943 + 1.836734694 Combine like terms: -3.147094943 + 1.836734694 = -1.310360249 t = -1.310360249 Simplifying t = -1.310360249Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.983829637, -1.310360249}
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