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Simplifying 0.0885t2 + -0.934t + 1.819 = 0 Reorder the terms: 1.819 + -0.934t + 0.0885t2 = 0 Solving 1.819 + -0.934t + 0.0885t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 0.0885 the coefficient of the squared term: Divide each side by '0.0885'. 20.55367232 + -10.55367232t + t2 = 0 Move the constant term to the right: Add '-20.55367232' to each side of the equation. 20.55367232 + -10.55367232t + -20.55367232 + t2 = 0 + -20.55367232 Reorder the terms: 20.55367232 + -20.55367232 + -10.55367232t + t2 = 0 + -20.55367232 Combine like terms: 20.55367232 + -20.55367232 = 0.00000000 0.00000000 + -10.55367232t + t2 = 0 + -20.55367232 -10.55367232t + t2 = 0 + -20.55367232 Combine like terms: 0 + -20.55367232 = -20.55367232 -10.55367232t + t2 = -20.55367232 The t term is -10.55367232t. Take half its coefficient (-5.27683616). Square it (27.84499986) and add it to both sides. Add '27.84499986' to each side of the equation. -10.55367232t + 27.84499986 + t2 = -20.55367232 + 27.84499986 Reorder the terms: 27.84499986 + -10.55367232t + t2 = -20.55367232 + 27.84499986 Combine like terms: -20.55367232 + 27.84499986 = 7.29132754 27.84499986 + -10.55367232t + t2 = 7.29132754 Factor a perfect square on the left side: (t + -5.27683616)(t + -5.27683616) = 7.29132754 Calculate the square root of the right side: 2.70024583 Break this problem into two subproblems by setting (t + -5.27683616) equal to 2.70024583 and -2.70024583.Subproblem 1
t + -5.27683616 = 2.70024583 Simplifying t + -5.27683616 = 2.70024583 Reorder the terms: -5.27683616 + t = 2.70024583 Solving -5.27683616 + t = 2.70024583 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.27683616' to each side of the equation. -5.27683616 + 5.27683616 + t = 2.70024583 + 5.27683616 Combine like terms: -5.27683616 + 5.27683616 = 0.00000000 0.00000000 + t = 2.70024583 + 5.27683616 t = 2.70024583 + 5.27683616 Combine like terms: 2.70024583 + 5.27683616 = 7.97708199 t = 7.97708199 Simplifying t = 7.97708199Subproblem 2
t + -5.27683616 = -2.70024583 Simplifying t + -5.27683616 = -2.70024583 Reorder the terms: -5.27683616 + t = -2.70024583 Solving -5.27683616 + t = -2.70024583 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.27683616' to each side of the equation. -5.27683616 + 5.27683616 + t = -2.70024583 + 5.27683616 Combine like terms: -5.27683616 + 5.27683616 = 0.00000000 0.00000000 + t = -2.70024583 + 5.27683616 t = -2.70024583 + 5.27683616 Combine like terms: -2.70024583 + 5.27683616 = 2.57659033 t = 2.57659033 Simplifying t = 2.57659033Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.97708199, 2.57659033}
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