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Simplifying -4.9t2 + 22.1t + 22.1 = 0 Reorder the terms: 22.1 + 22.1t + -4.9t2 = 0 Solving 22.1 + 22.1t + -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'. -4.510204082 + -4.510204082t + t2 = 0 Move the constant term to the right: Add '4.510204082' to each side of the equation. -4.510204082 + -4.510204082t + 4.510204082 + t2 = 0 + 4.510204082 Reorder the terms: -4.510204082 + 4.510204082 + -4.510204082t + t2 = 0 + 4.510204082 Combine like terms: -4.510204082 + 4.510204082 = 0.000000000 0.000000000 + -4.510204082t + t2 = 0 + 4.510204082 -4.510204082t + t2 = 0 + 4.510204082 Combine like terms: 0 + 4.510204082 = 4.510204082 -4.510204082t + t2 = 4.510204082 The t term is -4.510204082t. Take half its coefficient (-2.255102041). Square it (5.085485215) and add it to both sides. Add '5.085485215' to each side of the equation. -4.510204082t + 5.085485215 + t2 = 4.510204082 + 5.085485215 Reorder the terms: 5.085485215 + -4.510204082t + t2 = 4.510204082 + 5.085485215 Combine like terms: 4.510204082 + 5.085485215 = 9.595689297 5.085485215 + -4.510204082t + t2 = 9.595689297 Factor a perfect square on the left side: (t + -2.255102041)(t + -2.255102041) = 9.595689297 Calculate the square root of the right side: 3.097690962 Break this problem into two subproblems by setting (t + -2.255102041) equal to 3.097690962 and -3.097690962.Subproblem 1
t + -2.255102041 = 3.097690962 Simplifying t + -2.255102041 = 3.097690962 Reorder the terms: -2.255102041 + t = 3.097690962 Solving -2.255102041 + t = 3.097690962 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.255102041' to each side of the equation. -2.255102041 + 2.255102041 + t = 3.097690962 + 2.255102041 Combine like terms: -2.255102041 + 2.255102041 = 0.000000000 0.000000000 + t = 3.097690962 + 2.255102041 t = 3.097690962 + 2.255102041 Combine like terms: 3.097690962 + 2.255102041 = 5.352793003 t = 5.352793003 Simplifying t = 5.352793003Subproblem 2
t + -2.255102041 = -3.097690962 Simplifying t + -2.255102041 = -3.097690962 Reorder the terms: -2.255102041 + t = -3.097690962 Solving -2.255102041 + t = -3.097690962 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.255102041' to each side of the equation. -2.255102041 + 2.255102041 + t = -3.097690962 + 2.255102041 Combine like terms: -2.255102041 + 2.255102041 = 0.000000000 0.000000000 + t = -3.097690962 + 2.255102041 t = -3.097690962 + 2.255102041 Combine like terms: -3.097690962 + 2.255102041 = -0.842588921 t = -0.842588921 Simplifying t = -0.842588921Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.352793003, -0.842588921}
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