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Simplifying 0 = -4.9t2 + 25t + 12 Reorder the terms: 0 = 12 + 25t + -4.9t2 Solving 0 = 12 + 25t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -12 = -12 -12 + -25t + 4.9t2 = 12 + 25t + -4.9t2 + -12 + -25t + 4.9t2 Reorder the terms: -12 + -25t + 4.9t2 = 12 + -12 + 25t + -25t + -4.9t2 + 4.9t2 Combine like terms: 12 + -12 = 0 -12 + -25t + 4.9t2 = 0 + 25t + -25t + -4.9t2 + 4.9t2 -12 + -25t + 4.9t2 = 25t + -25t + -4.9t2 + 4.9t2 Combine like terms: 25t + -25t = 0 -12 + -25t + 4.9t2 = 0 + -4.9t2 + 4.9t2 -12 + -25t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -12 + -25t + 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'. -2.448979592 + -5.102040816t + t2 = 0 Move the constant term to the right: Add '2.448979592' to each side of the equation. -2.448979592 + -5.102040816t + 2.448979592 + t2 = 0 + 2.448979592 Reorder the terms: -2.448979592 + 2.448979592 + -5.102040816t + t2 = 0 + 2.448979592 Combine like terms: -2.448979592 + 2.448979592 = 0.000000000 0.000000000 + -5.102040816t + t2 = 0 + 2.448979592 -5.102040816t + t2 = 0 + 2.448979592 Combine like terms: 0 + 2.448979592 = 2.448979592 -5.102040816t + t2 = 2.448979592 The t term is -5.102040816t. Take half its coefficient (-2.551020408). Square it (6.507705122) and add it to both sides. Add '6.507705122' to each side of the equation. -5.102040816t + 6.507705122 + t2 = 2.448979592 + 6.507705122 Reorder the terms: 6.507705122 + -5.102040816t + t2 = 2.448979592 + 6.507705122 Combine like terms: 2.448979592 + 6.507705122 = 8.956684714 6.507705122 + -5.102040816t + t2 = 8.956684714 Factor a perfect square on the left side: (t + -2.551020408)(t + -2.551020408) = 8.956684714 Calculate the square root of the right side: 2.992772079 Break this problem into two subproblems by setting (t + -2.551020408) equal to 2.992772079 and -2.992772079.Subproblem 1
t + -2.551020408 = 2.992772079 Simplifying t + -2.551020408 = 2.992772079 Reorder the terms: -2.551020408 + t = 2.992772079 Solving -2.551020408 + t = 2.992772079 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.551020408' to each side of the equation. -2.551020408 + 2.551020408 + t = 2.992772079 + 2.551020408 Combine like terms: -2.551020408 + 2.551020408 = 0.000000000 0.000000000 + t = 2.992772079 + 2.551020408 t = 2.992772079 + 2.551020408 Combine like terms: 2.992772079 + 2.551020408 = 5.543792487 t = 5.543792487 Simplifying t = 5.543792487Subproblem 2
t + -2.551020408 = -2.992772079 Simplifying t + -2.551020408 = -2.992772079 Reorder the terms: -2.551020408 + t = -2.992772079 Solving -2.551020408 + t = -2.992772079 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.551020408' to each side of the equation. -2.551020408 + 2.551020408 + t = -2.992772079 + 2.551020408 Combine like terms: -2.551020408 + 2.551020408 = 0.000000000 0.000000000 + t = -2.992772079 + 2.551020408 t = -2.992772079 + 2.551020408 Combine like terms: -2.992772079 + 2.551020408 = -0.441751671 t = -0.441751671 Simplifying t = -0.441751671Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.543792487, -0.441751671}
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