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Simplifying 295 = 28t + -0.4t2 Solving 295 = 28t + -0.4t2 Solving for variable 't'. Reorder the terms: 295 + -28t + 0.4t2 = 28t + -28t + -0.4t2 + 0.4t2 Combine like terms: 28t + -28t = 0 295 + -28t + 0.4t2 = 0 + -0.4t2 + 0.4t2 295 + -28t + 0.4t2 = -0.4t2 + 0.4t2 Combine like terms: -0.4t2 + 0.4t2 = 0.0 295 + -28t + 0.4t2 = 0.0 Begin completing the square. Divide all terms by 0.4 the coefficient of the squared term: Divide each side by '0.4'. 737.5 + -70t + t2 = 0 Move the constant term to the right: Add '-737.5' to each side of the equation. 737.5 + -70t + -737.5 + t2 = 0 + -737.5 Reorder the terms: 737.5 + -737.5 + -70t + t2 = 0 + -737.5 Combine like terms: 737.5 + -737.5 = 0.0 0.0 + -70t + t2 = 0 + -737.5 -70t + t2 = 0 + -737.5 Combine like terms: 0 + -737.5 = -737.5 -70t + t2 = -737.5 The t term is -70t. Take half its coefficient (-35). Square it (1225) and add it to both sides. Add '1225' to each side of the equation. -70t + 1225 + t2 = -737.5 + 1225 Reorder the terms: 1225 + -70t + t2 = -737.5 + 1225 Combine like terms: -737.5 + 1225 = 487.5 1225 + -70t + t2 = 487.5 Factor a perfect square on the left side: (t + -35)(t + -35) = 487.5 Calculate the square root of the right side: 22.079402166 Break this problem into two subproblems by setting (t + -35) equal to 22.079402166 and -22.079402166.Subproblem 1
t + -35 = 22.079402166 Simplifying t + -35 = 22.079402166 Reorder the terms: -35 + t = 22.079402166 Solving -35 + t = 22.079402166 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '35' to each side of the equation. -35 + 35 + t = 22.079402166 + 35 Combine like terms: -35 + 35 = 0 0 + t = 22.079402166 + 35 t = 22.079402166 + 35 Combine like terms: 22.079402166 + 35 = 57.079402166 t = 57.079402166 Simplifying t = 57.079402166Subproblem 2
t + -35 = -22.079402166 Simplifying t + -35 = -22.079402166 Reorder the terms: -35 + t = -22.079402166 Solving -35 + t = -22.079402166 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '35' to each side of the equation. -35 + 35 + t = -22.079402166 + 35 Combine like terms: -35 + 35 = 0 0 + t = -22.079402166 + 35 t = -22.079402166 + 35 Combine like terms: -22.079402166 + 35 = 12.920597834 t = 12.920597834 Simplifying t = 12.920597834Solution
The solution to the problem is based on the solutions from the subproblems. t = {57.079402166, 12.920597834}
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