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Simplifying 79.2t + 2.05t2 + -1140 = 0 Reorder the terms: -1140 + 79.2t + 2.05t2 = 0 Solving -1140 + 79.2t + 2.05t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 2.05 the coefficient of the squared term: Divide each side by '2.05'. -556.097561 + 38.63414634t + t2 = 0 Move the constant term to the right: Add '556.097561' to each side of the equation. -556.097561 + 38.63414634t + 556.097561 + t2 = 0 + 556.097561 Reorder the terms: -556.097561 + 556.097561 + 38.63414634t + t2 = 0 + 556.097561 Combine like terms: -556.097561 + 556.097561 = 0.000000 0.000000 + 38.63414634t + t2 = 0 + 556.097561 38.63414634t + t2 = 0 + 556.097561 Combine like terms: 0 + 556.097561 = 556.097561 38.63414634t + t2 = 556.097561 The t term is 38.63414634t. Take half its coefficient (19.31707317). Square it (373.1493159) and add it to both sides. Add '373.1493159' to each side of the equation. 38.63414634t + 373.1493159 + t2 = 556.097561 + 373.1493159 Reorder the terms: 373.1493159 + 38.63414634t + t2 = 556.097561 + 373.1493159 Combine like terms: 556.097561 + 373.1493159 = 929.2468769 373.1493159 + 38.63414634t + t2 = 929.2468769 Factor a perfect square on the left side: (t + 19.31707317)(t + 19.31707317) = 929.2468769 Calculate the square root of the right side: 30.483550923 Break this problem into two subproblems by setting (t + 19.31707317) equal to 30.483550923 and -30.483550923.Subproblem 1
t + 19.31707317 = 30.483550923 Simplifying t + 19.31707317 = 30.483550923 Reorder the terms: 19.31707317 + t = 30.483550923 Solving 19.31707317 + t = 30.483550923 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-19.31707317' to each side of the equation. 19.31707317 + -19.31707317 + t = 30.483550923 + -19.31707317 Combine like terms: 19.31707317 + -19.31707317 = 0.00000000 0.00000000 + t = 30.483550923 + -19.31707317 t = 30.483550923 + -19.31707317 Combine like terms: 30.483550923 + -19.31707317 = 11.166477753 t = 11.166477753 Simplifying t = 11.166477753Subproblem 2
t + 19.31707317 = -30.483550923 Simplifying t + 19.31707317 = -30.483550923 Reorder the terms: 19.31707317 + t = -30.483550923 Solving 19.31707317 + t = -30.483550923 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-19.31707317' to each side of the equation. 19.31707317 + -19.31707317 + t = -30.483550923 + -19.31707317 Combine like terms: 19.31707317 + -19.31707317 = 0.00000000 0.00000000 + t = -30.483550923 + -19.31707317 t = -30.483550923 + -19.31707317 Combine like terms: -30.483550923 + -19.31707317 = -49.800624093 t = -49.800624093 Simplifying t = -49.800624093Solution
The solution to the problem is based on the solutions from the subproblems. t = {11.166477753, -49.800624093}
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