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Simplifying 0 = 0.45t2 + 18t + -75 Reorder the terms: 0 = -75 + 18t + 0.45t2 Solving 0 = -75 + 18t + 0.45t2 Solving for variable 't'. Combine like terms: 0 + 75 = 75 75 + -18t + -0.45t2 = -75 + 18t + 0.45t2 + 75 + -18t + -0.45t2 Reorder the terms: 75 + -18t + -0.45t2 = -75 + 75 + 18t + -18t + 0.45t2 + -0.45t2 Combine like terms: -75 + 75 = 0 75 + -18t + -0.45t2 = 0 + 18t + -18t + 0.45t2 + -0.45t2 75 + -18t + -0.45t2 = 18t + -18t + 0.45t2 + -0.45t2 Combine like terms: 18t + -18t = 0 75 + -18t + -0.45t2 = 0 + 0.45t2 + -0.45t2 75 + -18t + -0.45t2 = 0.45t2 + -0.45t2 Combine like terms: 0.45t2 + -0.45t2 = 0.00 75 + -18t + -0.45t2 = 0.00 Begin completing the square. Divide all terms by -0.45 the coefficient of the squared term: Divide each side by '-0.45'. -166.6666667 + 40t + t2 = 0 Move the constant term to the right: Add '166.6666667' to each side of the equation. -166.6666667 + 40t + 166.6666667 + t2 = 0 + 166.6666667 Reorder the terms: -166.6666667 + 166.6666667 + 40t + t2 = 0 + 166.6666667 Combine like terms: -166.6666667 + 166.6666667 = 0.0000000 0.0000000 + 40t + t2 = 0 + 166.6666667 40t + t2 = 0 + 166.6666667 Combine like terms: 0 + 166.6666667 = 166.6666667 40t + t2 = 166.6666667 The t term is 40t. Take half its coefficient (20). Square it (400) and add it to both sides. Add '400' to each side of the equation. 40t + 400 + t2 = 166.6666667 + 400 Reorder the terms: 400 + 40t + t2 = 166.6666667 + 400 Combine like terms: 166.6666667 + 400 = 566.6666667 400 + 40t + t2 = 566.6666667 Factor a perfect square on the left side: (t + 20)(t + 20) = 566.6666667 Calculate the square root of the right side: 23.804761429 Break this problem into two subproblems by setting (t + 20) equal to 23.804761429 and -23.804761429.Subproblem 1
t + 20 = 23.804761429 Simplifying t + 20 = 23.804761429 Reorder the terms: 20 + t = 23.804761429 Solving 20 + t = 23.804761429 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + t = 23.804761429 + -20 Combine like terms: 20 + -20 = 0 0 + t = 23.804761429 + -20 t = 23.804761429 + -20 Combine like terms: 23.804761429 + -20 = 3.804761429 t = 3.804761429 Simplifying t = 3.804761429Subproblem 2
t + 20 = -23.804761429 Simplifying t + 20 = -23.804761429 Reorder the terms: 20 + t = -23.804761429 Solving 20 + t = -23.804761429 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + t = -23.804761429 + -20 Combine like terms: 20 + -20 = 0 0 + t = -23.804761429 + -20 t = -23.804761429 + -20 Combine like terms: -23.804761429 + -20 = -43.804761429 t = -43.804761429 Simplifying t = -43.804761429Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.804761429, -43.804761429}
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