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Simplifying 1.1t2 + 100t + -100 = 0 Reorder the terms: -100 + 100t + 1.1t2 = 0 Solving -100 + 100t + 1.1t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 1.1 the coefficient of the squared term: Divide each side by '1.1'. -90.90909091 + 90.90909091t + t2 = 0 Move the constant term to the right: Add '90.90909091' to each side of the equation. -90.90909091 + 90.90909091t + 90.90909091 + t2 = 0 + 90.90909091 Reorder the terms: -90.90909091 + 90.90909091 + 90.90909091t + t2 = 0 + 90.90909091 Combine like terms: -90.90909091 + 90.90909091 = 0.00000000 0.00000000 + 90.90909091t + t2 = 0 + 90.90909091 90.90909091t + t2 = 0 + 90.90909091 Combine like terms: 0 + 90.90909091 = 90.90909091 90.90909091t + t2 = 90.90909091 The t term is 90.90909091t. Take half its coefficient (45.45454546). Square it (2066.115703) and add it to both sides. Add '2066.115703' to each side of the equation. 90.90909091t + 2066.115703 + t2 = 90.90909091 + 2066.115703 Reorder the terms: 2066.115703 + 90.90909091t + t2 = 90.90909091 + 2066.115703 Combine like terms: 90.90909091 + 2066.115703 = 2157.02479391 2066.115703 + 90.90909091t + t2 = 2157.02479391 Factor a perfect square on the left side: (t + 45.45454546)(t + 45.45454546) = 2157.02479391 Calculate the square root of the right side: 46.443781004 Break this problem into two subproblems by setting (t + 45.45454546) equal to 46.443781004 and -46.443781004.Subproblem 1
t + 45.45454546 = 46.443781004 Simplifying t + 45.45454546 = 46.443781004 Reorder the terms: 45.45454546 + t = 46.443781004 Solving 45.45454546 + t = 46.443781004 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-45.45454546' to each side of the equation. 45.45454546 + -45.45454546 + t = 46.443781004 + -45.45454546 Combine like terms: 45.45454546 + -45.45454546 = 0.00000000 0.00000000 + t = 46.443781004 + -45.45454546 t = 46.443781004 + -45.45454546 Combine like terms: 46.443781004 + -45.45454546 = 0.989235544 t = 0.989235544 Simplifying t = 0.989235544Subproblem 2
t + 45.45454546 = -46.443781004 Simplifying t + 45.45454546 = -46.443781004 Reorder the terms: 45.45454546 + t = -46.443781004 Solving 45.45454546 + t = -46.443781004 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-45.45454546' to each side of the equation. 45.45454546 + -45.45454546 + t = -46.443781004 + -45.45454546 Combine like terms: 45.45454546 + -45.45454546 = 0.00000000 0.00000000 + t = -46.443781004 + -45.45454546 t = -46.443781004 + -45.45454546 Combine like terms: -46.443781004 + -45.45454546 = -91.898326464 t = -91.898326464 Simplifying t = -91.898326464Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.989235544, -91.898326464}
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