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Simplifying 2.5 = 18t + 4.9t2 Solving 2.5 = 18t + 4.9t2 Solving for variable 't'. Reorder the terms: 2.5 + -18t + -4.9t2 = 18t + -18t + 4.9t2 + -4.9t2 Combine like terms: 18t + -18t = 0 2.5 + -18t + -4.9t2 = 0 + 4.9t2 + -4.9t2 2.5 + -18t + -4.9t2 = 4.9t2 + -4.9t2 Combine like terms: 4.9t2 + -4.9t2 = 0.0 2.5 + -18t + -4.9t2 = 0.0 Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -0.5102040816 + 3.673469388t + t2 = 0 Move the constant term to the right: Add '0.5102040816' to each side of the equation. -0.5102040816 + 3.673469388t + 0.5102040816 + t2 = 0 + 0.5102040816 Reorder the terms: -0.5102040816 + 0.5102040816 + 3.673469388t + t2 = 0 + 0.5102040816 Combine like terms: -0.5102040816 + 0.5102040816 = 0.0000000000 0.0000000000 + 3.673469388t + t2 = 0 + 0.5102040816 3.673469388t + t2 = 0 + 0.5102040816 Combine like terms: 0 + 0.5102040816 = 0.5102040816 3.673469388t + t2 = 0.5102040816 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 = 0.5102040816 + 3.373594336 Reorder the terms: 3.373594336 + 3.673469388t + t2 = 0.5102040816 + 3.373594336 Combine like terms: 0.5102040816 + 3.373594336 = 3.8837984176 3.373594336 + 3.673469388t + t2 = 3.8837984176 Factor a perfect square on the left side: (t + 1.836734694)(t + 1.836734694) = 3.8837984176 Calculate the square root of the right side: 1.970735502 Break this problem into two subproblems by setting (t + 1.836734694) equal to 1.970735502 and -1.970735502.Subproblem 1
t + 1.836734694 = 1.970735502 Simplifying t + 1.836734694 = 1.970735502 Reorder the terms: 1.836734694 + t = 1.970735502 Solving 1.836734694 + t = 1.970735502 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 = 1.970735502 + -1.836734694 Combine like terms: 1.836734694 + -1.836734694 = 0.000000000 0.000000000 + t = 1.970735502 + -1.836734694 t = 1.970735502 + -1.836734694 Combine like terms: 1.970735502 + -1.836734694 = 0.134000808 t = 0.134000808 Simplifying t = 0.134000808Subproblem 2
t + 1.836734694 = -1.970735502 Simplifying t + 1.836734694 = -1.970735502 Reorder the terms: 1.836734694 + t = -1.970735502 Solving 1.836734694 + t = -1.970735502 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 = -1.970735502 + -1.836734694 Combine like terms: 1.836734694 + -1.836734694 = 0.000000000 0.000000000 + t = -1.970735502 + -1.836734694 t = -1.970735502 + -1.836734694 Combine like terms: -1.970735502 + -1.836734694 = -3.807470196 t = -3.807470196 Simplifying t = -3.807470196Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.134000808, -3.807470196}
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