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Simplifying 0 = 100 + 25t + -4.9t2 Solving 0 = 100 + 25t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -100 = -100 -100 + -25t + 4.9t2 = 100 + 25t + -4.9t2 + -100 + -25t + 4.9t2 Reorder the terms: -100 + -25t + 4.9t2 = 100 + -100 + 25t + -25t + -4.9t2 + 4.9t2 Combine like terms: 100 + -100 = 0 -100 + -25t + 4.9t2 = 0 + 25t + -25t + -4.9t2 + 4.9t2 -100 + -25t + 4.9t2 = 25t + -25t + -4.9t2 + 4.9t2 Combine like terms: 25t + -25t = 0 -100 + -25t + 4.9t2 = 0 + -4.9t2 + 4.9t2 -100 + -25t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -100 + -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'. -20.40816327 + -5.102040816t + t2 = 0 Move the constant term to the right: Add '20.40816327' to each side of the equation. -20.40816327 + -5.102040816t + 20.40816327 + t2 = 0 + 20.40816327 Reorder the terms: -20.40816327 + 20.40816327 + -5.102040816t + t2 = 0 + 20.40816327 Combine like terms: -20.40816327 + 20.40816327 = 0.00000000 0.00000000 + -5.102040816t + t2 = 0 + 20.40816327 -5.102040816t + t2 = 0 + 20.40816327 Combine like terms: 0 + 20.40816327 = 20.40816327 -5.102040816t + t2 = 20.40816327 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 = 20.40816327 + 6.507705122 Reorder the terms: 6.507705122 + -5.102040816t + t2 = 20.40816327 + 6.507705122 Combine like terms: 20.40816327 + 6.507705122 = 26.915868392 6.507705122 + -5.102040816t + t2 = 26.915868392 Factor a perfect square on the left side: (t + -2.551020408)(t + -2.551020408) = 26.915868392 Calculate the square root of the right side: 5.188050539 Break this problem into two subproblems by setting (t + -2.551020408) equal to 5.188050539 and -5.188050539.Subproblem 1
t + -2.551020408 = 5.188050539 Simplifying t + -2.551020408 = 5.188050539 Reorder the terms: -2.551020408 + t = 5.188050539 Solving -2.551020408 + t = 5.188050539 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 = 5.188050539 + 2.551020408 Combine like terms: -2.551020408 + 2.551020408 = 0.000000000 0.000000000 + t = 5.188050539 + 2.551020408 t = 5.188050539 + 2.551020408 Combine like terms: 5.188050539 + 2.551020408 = 7.739070947 t = 7.739070947 Simplifying t = 7.739070947Subproblem 2
t + -2.551020408 = -5.188050539 Simplifying t + -2.551020408 = -5.188050539 Reorder the terms: -2.551020408 + t = -5.188050539 Solving -2.551020408 + t = -5.188050539 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 = -5.188050539 + 2.551020408 Combine like terms: -2.551020408 + 2.551020408 = 0.000000000 0.000000000 + t = -5.188050539 + 2.551020408 t = -5.188050539 + 2.551020408 Combine like terms: -5.188050539 + 2.551020408 = -2.637030131 t = -2.637030131 Simplifying t = -2.637030131Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.739070947, -2.637030131}
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