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Simplifying 0.0885t2 + -0.932t + 1.782 = 0 Reorder the terms: 1.782 + -0.932t + 0.0885t2 = 0 Solving 1.782 + -0.932t + 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'. 20.13559322 + -10.53107345t + t2 = 0 Move the constant term to the right: Add '-20.13559322' to each side of the equation. 20.13559322 + -10.53107345t + -20.13559322 + t2 = 0 + -20.13559322 Reorder the terms: 20.13559322 + -20.13559322 + -10.53107345t + t2 = 0 + -20.13559322 Combine like terms: 20.13559322 + -20.13559322 = 0.00000000 0.00000000 + -10.53107345t + t2 = 0 + -20.13559322 -10.53107345t + t2 = 0 + -20.13559322 Combine like terms: 0 + -20.13559322 = -20.13559322 -10.53107345t + t2 = -20.13559322 The t term is -10.53107345t. Take half its coefficient (-5.265536725). Square it (27.72587700) and add it to both sides. Add '27.72587700' to each side of the equation. -10.53107345t + 27.72587700 + t2 = -20.13559322 + 27.72587700 Reorder the terms: 27.72587700 + -10.53107345t + t2 = -20.13559322 + 27.72587700 Combine like terms: -20.13559322 + 27.72587700 = 7.59028378 27.72587700 + -10.53107345t + t2 = 7.59028378 Factor a perfect square on the left side: (t + -5.265536725)(t + -5.265536725) = 7.59028378 Calculate the square root of the right side: 2.755046965 Break this problem into two subproblems by setting (t + -5.265536725) equal to 2.755046965 and -2.755046965.Subproblem 1
t + -5.265536725 = 2.755046965 Simplifying t + -5.265536725 = 2.755046965 Reorder the terms: -5.265536725 + t = 2.755046965 Solving -5.265536725 + t = 2.755046965 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.265536725' to each side of the equation. -5.265536725 + 5.265536725 + t = 2.755046965 + 5.265536725 Combine like terms: -5.265536725 + 5.265536725 = 0.000000000 0.000000000 + t = 2.755046965 + 5.265536725 t = 2.755046965 + 5.265536725 Combine like terms: 2.755046965 + 5.265536725 = 8.02058369 t = 8.02058369 Simplifying t = 8.02058369Subproblem 2
t + -5.265536725 = -2.755046965 Simplifying t + -5.265536725 = -2.755046965 Reorder the terms: -5.265536725 + t = -2.755046965 Solving -5.265536725 + t = -2.755046965 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.265536725' to each side of the equation. -5.265536725 + 5.265536725 + t = -2.755046965 + 5.265536725 Combine like terms: -5.265536725 + 5.265536725 = 0.000000000 0.000000000 + t = -2.755046965 + 5.265536725 t = -2.755046965 + 5.265536725 Combine like terms: -2.755046965 + 5.265536725 = 2.51048976 t = 2.51048976 Simplifying t = 2.51048976Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.02058369, 2.51048976}
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