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Simplifying 122.4 = 20.8T + -0.8T2 Solving 122.4 = 20.8T + -0.8T2 Solving for variable 'T'. Reorder the terms: 122.4 + -20.8T + 0.8T2 = 20.8T + -20.8T + -0.8T2 + 0.8T2 Combine like terms: 20.8T + -20.8T = 0.0 122.4 + -20.8T + 0.8T2 = 0.0 + -0.8T2 + 0.8T2 122.4 + -20.8T + 0.8T2 = -0.8T2 + 0.8T2 Combine like terms: -0.8T2 + 0.8T2 = 0.0 122.4 + -20.8T + 0.8T2 = 0.0 Begin completing the square. Divide all terms by 0.8 the coefficient of the squared term: Divide each side by '0.8'. 153 + -26T + T2 = 0 Move the constant term to the right: Add '-153' to each side of the equation. 153 + -26T + -153 + T2 = 0 + -153 Reorder the terms: 153 + -153 + -26T + T2 = 0 + -153 Combine like terms: 153 + -153 = 0 0 + -26T + T2 = 0 + -153 -26T + T2 = 0 + -153 Combine like terms: 0 + -153 = -153 -26T + T2 = -153 The T term is -26T. Take half its coefficient (-13). Square it (169) and add it to both sides. Add '169' to each side of the equation. -26T + 169 + T2 = -153 + 169 Reorder the terms: 169 + -26T + T2 = -153 + 169 Combine like terms: -153 + 169 = 16 169 + -26T + T2 = 16 Factor a perfect square on the left side: (T + -13)(T + -13) = 16 Calculate the square root of the right side: 4 Break this problem into two subproblems by setting (T + -13) equal to 4 and -4.Subproblem 1
T + -13 = 4 Simplifying T + -13 = 4 Reorder the terms: -13 + T = 4 Solving -13 + T = 4 Solving for variable 'T'. Move all terms containing T to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + T = 4 + 13 Combine like terms: -13 + 13 = 0 0 + T = 4 + 13 T = 4 + 13 Combine like terms: 4 + 13 = 17 T = 17 Simplifying T = 17Subproblem 2
T + -13 = -4 Simplifying T + -13 = -4 Reorder the terms: -13 + T = -4 Solving -13 + T = -4 Solving for variable 'T'. Move all terms containing T to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + T = -4 + 13 Combine like terms: -13 + 13 = 0 0 + T = -4 + 13 T = -4 + 13 Combine like terms: -4 + 13 = 9 T = 9 Simplifying T = 9Solution
The solution to the problem is based on the solutions from the subproblems. T = {17, 9}
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