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Simplifying 1 = 4.9t2 + -3.5t + -10 Reorder the terms: 1 = -10 + -3.5t + 4.9t2 Solving 1 = -10 + -3.5t + 4.9t2 Solving for variable 't'. Combine like terms: 1 + 10 = 11 11 + 3.5t + -4.9t2 = -10 + -3.5t + 4.9t2 + 10 + 3.5t + -4.9t2 Reorder the terms: 11 + 3.5t + -4.9t2 = -10 + 10 + -3.5t + 3.5t + 4.9t2 + -4.9t2 Combine like terms: -10 + 10 = 0 11 + 3.5t + -4.9t2 = 0 + -3.5t + 3.5t + 4.9t2 + -4.9t2 11 + 3.5t + -4.9t2 = -3.5t + 3.5t + 4.9t2 + -4.9t2 Combine like terms: -3.5t + 3.5t = 0.0 11 + 3.5t + -4.9t2 = 0.0 + 4.9t2 + -4.9t2 11 + 3.5t + -4.9t2 = 4.9t2 + -4.9t2 Combine like terms: 4.9t2 + -4.9t2 = 0.0 11 + 3.5t + -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'. -2.244897959 + -0.7142857143t + t2 = 0 Move the constant term to the right: Add '2.244897959' to each side of the equation. -2.244897959 + -0.7142857143t + 2.244897959 + t2 = 0 + 2.244897959 Reorder the terms: -2.244897959 + 2.244897959 + -0.7142857143t + t2 = 0 + 2.244897959 Combine like terms: -2.244897959 + 2.244897959 = 0.000000000 0.000000000 + -0.7142857143t + t2 = 0 + 2.244897959 -0.7142857143t + t2 = 0 + 2.244897959 Combine like terms: 0 + 2.244897959 = 2.244897959 -0.7142857143t + t2 = 2.244897959 The t term is -0.7142857143t. Take half its coefficient (-0.3571428572). Square it (0.1275510204) and add it to both sides. Add '0.1275510204' to each side of the equation. -0.7142857143t + 0.1275510204 + t2 = 2.244897959 + 0.1275510204 Reorder the terms: 0.1275510204 + -0.7142857143t + t2 = 2.244897959 + 0.1275510204 Combine like terms: 2.244897959 + 0.1275510204 = 2.3724489794 0.1275510204 + -0.7142857143t + t2 = 2.3724489794 Factor a perfect square on the left side: (t + -0.3571428572)(t + -0.3571428572) = 2.3724489794 Calculate the square root of the right side: 1.540275618 Break this problem into two subproblems by setting (t + -0.3571428572) equal to 1.540275618 and -1.540275618.Subproblem 1
t + -0.3571428572 = 1.540275618 Simplifying t + -0.3571428572 = 1.540275618 Reorder the terms: -0.3571428572 + t = 1.540275618 Solving -0.3571428572 + t = 1.540275618 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.3571428572' to each side of the equation. -0.3571428572 + 0.3571428572 + t = 1.540275618 + 0.3571428572 Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000 0.0000000000 + t = 1.540275618 + 0.3571428572 t = 1.540275618 + 0.3571428572 Combine like terms: 1.540275618 + 0.3571428572 = 1.8974184752 t = 1.8974184752 Simplifying t = 1.8974184752Subproblem 2
t + -0.3571428572 = -1.540275618 Simplifying t + -0.3571428572 = -1.540275618 Reorder the terms: -0.3571428572 + t = -1.540275618 Solving -0.3571428572 + t = -1.540275618 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.3571428572' to each side of the equation. -0.3571428572 + 0.3571428572 + t = -1.540275618 + 0.3571428572 Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000 0.0000000000 + t = -1.540275618 + 0.3571428572 t = -1.540275618 + 0.3571428572 Combine like terms: -1.540275618 + 0.3571428572 = -1.1831327608 t = -1.1831327608 Simplifying t = -1.1831327608Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.8974184752, -1.1831327608}
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