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Simplifying 3 = 160T + -16T2 Solving 3 = 160T + -16T2 Solving for variable 'T'. Reorder the terms: 3 + -160T + 16T2 = 160T + -160T + -16T2 + 16T2 Combine like terms: 160T + -160T = 0 3 + -160T + 16T2 = 0 + -16T2 + 16T2 3 + -160T + 16T2 = -16T2 + 16T2 Combine like terms: -16T2 + 16T2 = 0 3 + -160T + 16T2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.1875 + -10T + T2 = 0 Move the constant term to the right: Add '-0.1875' to each side of the equation. 0.1875 + -10T + -0.1875 + T2 = 0 + -0.1875 Reorder the terms: 0.1875 + -0.1875 + -10T + T2 = 0 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + -10T + T2 = 0 + -0.1875 -10T + T2 = 0 + -0.1875 Combine like terms: 0 + -0.1875 = -0.1875 -10T + T2 = -0.1875 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 = -0.1875 + 25 Reorder the terms: 25 + -10T + T2 = -0.1875 + 25 Combine like terms: -0.1875 + 25 = 24.8125 25 + -10T + T2 = 24.8125 Factor a perfect square on the left side: (T + -5)(T + -5) = 24.8125 Calculate the square root of the right side: 4.981214711 Break this problem into two subproblems by setting (T + -5) equal to 4.981214711 and -4.981214711.Subproblem 1
T + -5 = 4.981214711 Simplifying T + -5 = 4.981214711 Reorder the terms: -5 + T = 4.981214711 Solving -5 + T = 4.981214711 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 = 4.981214711 + 5 Combine like terms: -5 + 5 = 0 0 + T = 4.981214711 + 5 T = 4.981214711 + 5 Combine like terms: 4.981214711 + 5 = 9.981214711 T = 9.981214711 Simplifying T = 9.981214711Subproblem 2
T + -5 = -4.981214711 Simplifying T + -5 = -4.981214711 Reorder the terms: -5 + T = -4.981214711 Solving -5 + T = -4.981214711 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 = -4.981214711 + 5 Combine like terms: -5 + 5 = 0 0 + T = -4.981214711 + 5 T = -4.981214711 + 5 Combine like terms: -4.981214711 + 5 = 0.018785289 T = 0.018785289 Simplifying T = 0.018785289Solution
The solution to the problem is based on the solutions from the subproblems. T = {9.981214711, 0.018785289}
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