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Simplifying 100 = (-4.9t2) + 49t + 1.5 Reorder the terms: 100 = 1.5 + 49t + (-4.9t2) Solving 100 = 1.5 + 49t + (-4.9t2) Solving for variable 't'. Combine like terms: 100 + -1.5 = 98.5 98.5 + -49t + (4.9t2) = 1.5 + 49t + (-4.9t2) + -1.5 + -49t + (4.9t2) Reorder the terms: 98.5 + -49t + (4.9t2) = 1.5 + -1.5 + 49t + -49t + (-4.9t2) + (4.9t2) Combine like terms: 1.5 + -1.5 = 0.0 98.5 + -49t + (4.9t2) = 0.0 + 49t + -49t + (-4.9t2) + (4.9t2) 98.5 + -49t + (4.9t2) = 49t + -49t + (-4.9t2) + (4.9t2) Combine like terms: 49t + -49t = 0 98.5 + -49t + (4.9t2) = 0 + (-4.9t2) + (4.9t2) 98.5 + -49t + (4.9t2) = (-4.9t2) + (4.9t2) Combine like terms: (-4.9t2) + (4.9t2) = 0.0 98.5 + -49t + (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'. 20.10204082 + -10t + t2 = 0 Move the constant term to the right: Add '-20.10204082' to each side of the equation. 20.10204082 + -10t + -20.10204082 + t2 = 0 + -20.10204082 Reorder the terms: 20.10204082 + -20.10204082 + -10t + t2 = 0 + -20.10204082 Combine like terms: 20.10204082 + -20.10204082 = 0.00000000 0.00000000 + -10t + t2 = 0 + -20.10204082 -10t + t2 = 0 + -20.10204082 Combine like terms: 0 + -20.10204082 = -20.10204082 -10t + t2 = -20.10204082 The t term is -10t. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10t + 25 + t2 = -20.10204082 + 25 Reorder the terms: 25 + -10t + t2 = -20.10204082 + 25 Combine like terms: -20.10204082 + 25 = 4.89795918 25 + -10t + t2 = 4.89795918 Factor a perfect square on the left side: ((t) + -5)((t) + -5) = 4.89795918 Calculate the square root of the right side: 2.21313334 Break this problem into two subproblems by setting ((t) + -5) equal to 2.21313334 and -2.21313334.Subproblem 1
(t) + -5 = 2.21313334 Simplifying (t) + -5 = 2.21313334 t + -5 = 2.21313334 Reorder the terms: -5 + t = 2.21313334 Solving -5 + t = 2.21313334 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + t = 2.21313334 + 5 Combine like terms: -5 + 5 = 0 0 + t = 2.21313334 + 5 t = 2.21313334 + 5 Combine like terms: 2.21313334 + 5 = 7.21313334 t = 7.21313334 Simplifying t = 7.21313334Subproblem 2
(t) + -5 = -2.21313334 Simplifying (t) + -5 = -2.21313334 t + -5 = -2.21313334 Reorder the terms: -5 + t = -2.21313334 Solving -5 + t = -2.21313334 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + t = -2.21313334 + 5 Combine like terms: -5 + 5 = 0 0 + t = -2.21313334 + 5 t = -2.21313334 + 5 Combine like terms: -2.21313334 + 5 = 2.78686666 t = 2.78686666 Simplifying t = 2.78686666Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.21313334, 2.78686666}
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