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Simplifying 35 = 0 + 7.5t + 4.9t2 Remove the zero: 35 = 7.5t + 4.9t2 Solving 35 = 7.5t + 4.9t2 Solving for variable 't'. Reorder the terms: 35 + -7.5t + -4.9t2 = 7.5t + -7.5t + 4.9t2 + -4.9t2 Combine like terms: 7.5t + -7.5t = 0.0 35 + -7.5t + -4.9t2 = 0.0 + 4.9t2 + -4.9t2 35 + -7.5t + -4.9t2 = 4.9t2 + -4.9t2 Combine like terms: 4.9t2 + -4.9t2 = 0.0 35 + -7.5t + -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'. -7.142857143 + 1.530612245t + t2 = 0 Move the constant term to the right: Add '7.142857143' to each side of the equation. -7.142857143 + 1.530612245t + 7.142857143 + t2 = 0 + 7.142857143 Reorder the terms: -7.142857143 + 7.142857143 + 1.530612245t + t2 = 0 + 7.142857143 Combine like terms: -7.142857143 + 7.142857143 = 0.000000000 0.000000000 + 1.530612245t + t2 = 0 + 7.142857143 1.530612245t + t2 = 0 + 7.142857143 Combine like terms: 0 + 7.142857143 = 7.142857143 1.530612245t + t2 = 7.142857143 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 = 7.142857143 + 0.5856934611 Reorder the terms: 0.5856934611 + 1.530612245t + t2 = 7.142857143 + 0.5856934611 Combine like terms: 7.142857143 + 0.5856934611 = 7.7285506041 0.5856934611 + 1.530612245t + t2 = 7.7285506041 Factor a perfect square on the left side: (t + 0.7653061225)(t + 0.7653061225) = 7.7285506041 Calculate the square root of the right side: 2.780027087 Break this problem into two subproblems by setting (t + 0.7653061225) equal to 2.780027087 and -2.780027087.Subproblem 1
t + 0.7653061225 = 2.780027087 Simplifying t + 0.7653061225 = 2.780027087 Reorder the terms: 0.7653061225 + t = 2.780027087 Solving 0.7653061225 + t = 2.780027087 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 = 2.780027087 + -0.7653061225 Combine like terms: 0.7653061225 + -0.7653061225 = 0.0000000000 0.0000000000 + t = 2.780027087 + -0.7653061225 t = 2.780027087 + -0.7653061225 Combine like terms: 2.780027087 + -0.7653061225 = 2.0147209645 t = 2.0147209645 Simplifying t = 2.0147209645Subproblem 2
t + 0.7653061225 = -2.780027087 Simplifying t + 0.7653061225 = -2.780027087 Reorder the terms: 0.7653061225 + t = -2.780027087 Solving 0.7653061225 + t = -2.780027087 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 = -2.780027087 + -0.7653061225 Combine like terms: 0.7653061225 + -0.7653061225 = 0.0000000000 0.0000000000 + t = -2.780027087 + -0.7653061225 t = -2.780027087 + -0.7653061225 Combine like terms: -2.780027087 + -0.7653061225 = -3.5453332095 t = -3.5453332095 Simplifying t = -3.5453332095Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.0147209645, -3.5453332095}
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