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Simplifying 30 = 42t + -4.9t2 Solving 30 = 42t + -4.9t2 Solving for variable 't'. Reorder the terms: 30 + -42t + 4.9t2 = 42t + -42t + -4.9t2 + 4.9t2 Combine like terms: 42t + -42t = 0 30 + -42t + 4.9t2 = 0 + -4.9t2 + 4.9t2 30 + -42t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 30 + -42t + 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'. 6.12244898 + -8.571428571t + t2 = 0 Move the constant term to the right: Add '-6.12244898' to each side of the equation. 6.12244898 + -8.571428571t + -6.12244898 + t2 = 0 + -6.12244898 Reorder the terms: 6.12244898 + -6.12244898 + -8.571428571t + t2 = 0 + -6.12244898 Combine like terms: 6.12244898 + -6.12244898 = 0.00000000 0.00000000 + -8.571428571t + t2 = 0 + -6.12244898 -8.571428571t + t2 = 0 + -6.12244898 Combine like terms: 0 + -6.12244898 = -6.12244898 -8.571428571t + t2 = -6.12244898 The t term is -8.571428571t. Take half its coefficient (-4.285714286). Square it (18.36734694) and add it to both sides. Add '18.36734694' to each side of the equation. -8.571428571t + 18.36734694 + t2 = -6.12244898 + 18.36734694 Reorder the terms: 18.36734694 + -8.571428571t + t2 = -6.12244898 + 18.36734694 Combine like terms: -6.12244898 + 18.36734694 = 12.24489796 18.36734694 + -8.571428571t + t2 = 12.24489796 Factor a perfect square on the left side: (t + -4.285714286)(t + -4.285714286) = 12.24489796 Calculate the square root of the right side: 3.499271061 Break this problem into two subproblems by setting (t + -4.285714286) equal to 3.499271061 and -3.499271061.Subproblem 1
t + -4.285714286 = 3.499271061 Simplifying t + -4.285714286 = 3.499271061 Reorder the terms: -4.285714286 + t = 3.499271061 Solving -4.285714286 + t = 3.499271061 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.285714286' to each side of the equation. -4.285714286 + 4.285714286 + t = 3.499271061 + 4.285714286 Combine like terms: -4.285714286 + 4.285714286 = 0.000000000 0.000000000 + t = 3.499271061 + 4.285714286 t = 3.499271061 + 4.285714286 Combine like terms: 3.499271061 + 4.285714286 = 7.784985347 t = 7.784985347 Simplifying t = 7.784985347Subproblem 2
t + -4.285714286 = -3.499271061 Simplifying t + -4.285714286 = -3.499271061 Reorder the terms: -4.285714286 + t = -3.499271061 Solving -4.285714286 + t = -3.499271061 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.285714286' to each side of the equation. -4.285714286 + 4.285714286 + t = -3.499271061 + 4.285714286 Combine like terms: -4.285714286 + 4.285714286 = 0.000000000 0.000000000 + t = -3.499271061 + 4.285714286 t = -3.499271061 + 4.285714286 Combine like terms: -3.499271061 + 4.285714286 = 0.786443225 t = 0.786443225 Simplifying t = 0.786443225Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.784985347, 0.786443225}
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