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Simplifying (0.5 * -9.8t2) + (371t) = 618 Multiply 0.5 * -9.8 (-4.9t2) + (371t) = 618 Reorder the terms: (371t) + (-4.9t2) = 618 Solving (371t) + (-4.9t2) = 618 Solving for variable 't'. Reorder the terms: -618 + (371t) + (-4.9t2) = 618 + -618 Combine like terms: 618 + -618 = 0 -618 + (371t) + (-4.9t2) = 0 Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. 126.122449 + (-75.71428571t) + t2 = 0 Move the constant term to the right: Add '-126.122449' to each side of the equation. 126.122449 + (-75.71428571t) + -126.122449 + t2 = 0 + -126.122449 Reorder the terms: 126.122449 + -126.122449 + (-75.71428571t) + t2 = 0 + -126.122449 Combine like terms: 126.122449 + -126.122449 = 0.000000 0.000000 + (-75.71428571t) + t2 = 0 + -126.122449 (-75.71428571t) + t2 = 0 + -126.122449 Combine like terms: 0 + -126.122449 = -126.122449 (-75.71428571t) + t2 = -126.122449 The t term is (-75.71428571t). Take half its coefficient (-37.85714286). Square it (1433.163266) and add it to both sides. Add '1433.163266' to each side of the equation. (-75.71428571t) + 1433.163266 + t2 = -126.122449 + 1433.163266 Reorder the terms: 1433.163266 + (-75.71428571t) + t2 = -126.122449 + 1433.163266 Combine like terms: -126.122449 + 1433.163266 = 1307.040817 1433.163266 + (-75.71428571t) + t2 = 1307.040817 Factor a perfect square on the left side: ((t) + -37.85714286)((t) + -37.85714286) = 1307.040817 Calculate the square root of the right side: 36.153019473 Break this problem into two subproblems by setting ((t) + -37.85714286) equal to 36.153019473 and -36.153019473.Subproblem 1
(t) + -37.85714286 = 36.153019473 Simplifying (t) + -37.85714286 = 36.153019473 t + -37.85714286 = 36.153019473 Reorder the terms: -37.85714286 + t = 36.153019473 Solving -37.85714286 + t = 36.153019473 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '37.85714286' to each side of the equation. -37.85714286 + 37.85714286 + t = 36.153019473 + 37.85714286 Combine like terms: -37.85714286 + 37.85714286 = 0.00000000 0.00000000 + t = 36.153019473 + 37.85714286 t = 36.153019473 + 37.85714286 Combine like terms: 36.153019473 + 37.85714286 = 74.010162333 t = 74.010162333 Simplifying t = 74.010162333Subproblem 2
(t) + -37.85714286 = -36.153019473 Simplifying (t) + -37.85714286 = -36.153019473 t + -37.85714286 = -36.153019473 Reorder the terms: -37.85714286 + t = -36.153019473 Solving -37.85714286 + t = -36.153019473 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '37.85714286' to each side of the equation. -37.85714286 + 37.85714286 + t = -36.153019473 + 37.85714286 Combine like terms: -37.85714286 + 37.85714286 = 0.00000000 0.00000000 + t = -36.153019473 + 37.85714286 t = -36.153019473 + 37.85714286 Combine like terms: -36.153019473 + 37.85714286 = 1.704123387 t = 1.704123387 Simplifying t = 1.704123387Solution
The solution to the problem is based on the solutions from the subproblems. t = {74.010162333, 1.704123387}
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