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Simplifying 0 = 95 + 7.50t + -4.9t2 Solving 0 = 95 + 7.50t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -95 = -95 -95 + -7.50t + 4.9t2 = 95 + 7.50t + -4.9t2 + -95 + -7.50t + 4.9t2 Reorder the terms: -95 + -7.50t + 4.9t2 = 95 + -95 + 7.50t + -7.50t + -4.9t2 + 4.9t2 Combine like terms: 95 + -95 = 0 -95 + -7.50t + 4.9t2 = 0 + 7.50t + -7.50t + -4.9t2 + 4.9t2 -95 + -7.50t + 4.9t2 = 7.50t + -7.50t + -4.9t2 + 4.9t2 Combine like terms: 7.50t + -7.50t = 0.00 -95 + -7.50t + 4.9t2 = 0.00 + -4.9t2 + 4.9t2 -95 + -7.50t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -95 + -7.50t + 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'. -19.3877551 + -1.530612245t + t2 = 0 Move the constant term to the right: Add '19.3877551' to each side of the equation. -19.3877551 + -1.530612245t + 19.3877551 + t2 = 0 + 19.3877551 Reorder the terms: -19.3877551 + 19.3877551 + -1.530612245t + t2 = 0 + 19.3877551 Combine like terms: -19.3877551 + 19.3877551 = 0.0000000 0.0000000 + -1.530612245t + t2 = 0 + 19.3877551 -1.530612245t + t2 = 0 + 19.3877551 Combine like terms: 0 + 19.3877551 = 19.3877551 -1.530612245t + t2 = 19.3877551 The t term is -1.530612245t. Take half its coefficient (-0.7653061225). Square it (0.5856934611) and add it to both sides. Add '0.5856934611' to each side of the equation. -1.530612245t + 0.5856934611 + t2 = 19.3877551 + 0.5856934611 Reorder the terms: 0.5856934611 + -1.530612245t + t2 = 19.3877551 + 0.5856934611 Combine like terms: 19.3877551 + 0.5856934611 = 19.9734485611 0.5856934611 + -1.530612245t + t2 = 19.9734485611 Factor a perfect square on the left side: (t + -0.7653061225)(t + -0.7653061225) = 19.9734485611 Calculate the square root of the right side: 4.469166428 Break this problem into two subproblems by setting (t + -0.7653061225) equal to 4.469166428 and -4.469166428.Subproblem 1
t + -0.7653061225 = 4.469166428 Simplifying t + -0.7653061225 = 4.469166428 Reorder the terms: -0.7653061225 + t = 4.469166428 Solving -0.7653061225 + t = 4.469166428 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.7653061225' to each side of the equation. -0.7653061225 + 0.7653061225 + t = 4.469166428 + 0.7653061225 Combine like terms: -0.7653061225 + 0.7653061225 = 0.0000000000 0.0000000000 + t = 4.469166428 + 0.7653061225 t = 4.469166428 + 0.7653061225 Combine like terms: 4.469166428 + 0.7653061225 = 5.2344725505 t = 5.2344725505 Simplifying t = 5.2344725505Subproblem 2
t + -0.7653061225 = -4.469166428 Simplifying t + -0.7653061225 = -4.469166428 Reorder the terms: -0.7653061225 + t = -4.469166428 Solving -0.7653061225 + t = -4.469166428 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.7653061225' to each side of the equation. -0.7653061225 + 0.7653061225 + t = -4.469166428 + 0.7653061225 Combine like terms: -0.7653061225 + 0.7653061225 = 0.0000000000 0.0000000000 + t = -4.469166428 + 0.7653061225 t = -4.469166428 + 0.7653061225 Combine like terms: -4.469166428 + 0.7653061225 = -3.7038603055 t = -3.7038603055 Simplifying t = -3.7038603055Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.2344725505, -3.7038603055}
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