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Simplifying -0.05t2 + 1.8t + 70 = 0 Reorder the terms: 70 + 1.8t + -0.05t2 = 0 Solving 70 + 1.8t + -0.05t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -0.05 the coefficient of the squared term: Divide each side by '-0.05'. -1400 + -36t + t2 = 0 Move the constant term to the right: Add '1400' to each side of the equation. -1400 + -36t + 1400 + t2 = 0 + 1400 Reorder the terms: -1400 + 1400 + -36t + t2 = 0 + 1400 Combine like terms: -1400 + 1400 = 0 0 + -36t + t2 = 0 + 1400 -36t + t2 = 0 + 1400 Combine like terms: 0 + 1400 = 1400 -36t + t2 = 1400 The t term is -36t. Take half its coefficient (-18). Square it (324) and add it to both sides. Add '324' to each side of the equation. -36t + 324 + t2 = 1400 + 324 Reorder the terms: 324 + -36t + t2 = 1400 + 324 Combine like terms: 1400 + 324 = 1724 324 + -36t + t2 = 1724 Factor a perfect square on the left side: (t + -18)(t + -18) = 1724 Calculate the square root of the right side: 41.521078984 Break this problem into two subproblems by setting (t + -18) equal to 41.521078984 and -41.521078984.Subproblem 1
t + -18 = 41.521078984 Simplifying t + -18 = 41.521078984 Reorder the terms: -18 + t = 41.521078984 Solving -18 + t = 41.521078984 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + t = 41.521078984 + 18 Combine like terms: -18 + 18 = 0 0 + t = 41.521078984 + 18 t = 41.521078984 + 18 Combine like terms: 41.521078984 + 18 = 59.521078984 t = 59.521078984 Simplifying t = 59.521078984Subproblem 2
t + -18 = -41.521078984 Simplifying t + -18 = -41.521078984 Reorder the terms: -18 + t = -41.521078984 Solving -18 + t = -41.521078984 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + t = -41.521078984 + 18 Combine like terms: -18 + 18 = 0 0 + t = -41.521078984 + 18 t = -41.521078984 + 18 Combine like terms: -41.521078984 + 18 = -23.521078984 t = -23.521078984 Simplifying t = -23.521078984Solution
The solution to the problem is based on the solutions from the subproblems. t = {59.521078984, -23.521078984}
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