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Simplifying 0 = 75 + 18.2t + -4.9t2 Solving 0 = 75 + 18.2t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -75 = -75 -75 + -18.2t + 4.9t2 = 75 + 18.2t + -4.9t2 + -75 + -18.2t + 4.9t2 Reorder the terms: -75 + -18.2t + 4.9t2 = 75 + -75 + 18.2t + -18.2t + -4.9t2 + 4.9t2 Combine like terms: 75 + -75 = 0 -75 + -18.2t + 4.9t2 = 0 + 18.2t + -18.2t + -4.9t2 + 4.9t2 -75 + -18.2t + 4.9t2 = 18.2t + -18.2t + -4.9t2 + 4.9t2 Combine like terms: 18.2t + -18.2t = 0.0 -75 + -18.2t + 4.9t2 = 0.0 + -4.9t2 + 4.9t2 -75 + -18.2t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -75 + -18.2t + 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'. -15.30612245 + -3.714285714t + t2 = 0 Move the constant term to the right: Add '15.30612245' to each side of the equation. -15.30612245 + -3.714285714t + 15.30612245 + t2 = 0 + 15.30612245 Reorder the terms: -15.30612245 + 15.30612245 + -3.714285714t + t2 = 0 + 15.30612245 Combine like terms: -15.30612245 + 15.30612245 = 0.00000000 0.00000000 + -3.714285714t + t2 = 0 + 15.30612245 -3.714285714t + t2 = 0 + 15.30612245 Combine like terms: 0 + 15.30612245 = 15.30612245 -3.714285714t + t2 = 15.30612245 The t term is -3.714285714t. Take half its coefficient (-1.857142857). Square it (3.448979591) and add it to both sides. Add '3.448979591' to each side of the equation. -3.714285714t + 3.448979591 + t2 = 15.30612245 + 3.448979591 Reorder the terms: 3.448979591 + -3.714285714t + t2 = 15.30612245 + 3.448979591 Combine like terms: 15.30612245 + 3.448979591 = 18.755102041 3.448979591 + -3.714285714t + t2 = 18.755102041 Factor a perfect square on the left side: (t + -1.857142857)(t + -1.857142857) = 18.755102041 Calculate the square root of the right side: 4.330716112 Break this problem into two subproblems by setting (t + -1.857142857) equal to 4.330716112 and -4.330716112.Subproblem 1
t + -1.857142857 = 4.330716112 Simplifying t + -1.857142857 = 4.330716112 Reorder the terms: -1.857142857 + t = 4.330716112 Solving -1.857142857 + t = 4.330716112 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.857142857' to each side of the equation. -1.857142857 + 1.857142857 + t = 4.330716112 + 1.857142857 Combine like terms: -1.857142857 + 1.857142857 = 0.000000000 0.000000000 + t = 4.330716112 + 1.857142857 t = 4.330716112 + 1.857142857 Combine like terms: 4.330716112 + 1.857142857 = 6.187858969 t = 6.187858969 Simplifying t = 6.187858969Subproblem 2
t + -1.857142857 = -4.330716112 Simplifying t + -1.857142857 = -4.330716112 Reorder the terms: -1.857142857 + t = -4.330716112 Solving -1.857142857 + t = -4.330716112 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.857142857' to each side of the equation. -1.857142857 + 1.857142857 + t = -4.330716112 + 1.857142857 Combine like terms: -1.857142857 + 1.857142857 = 0.000000000 0.000000000 + t = -4.330716112 + 1.857142857 t = -4.330716112 + 1.857142857 Combine like terms: -4.330716112 + 1.857142857 = -2.473573255 t = -2.473573255 Simplifying t = -2.473573255Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.187858969, -2.473573255}
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