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Simplifying 0.0825t2 + -0.886t + 1.752 = 0 Reorder the terms: 1.752 + -0.886t + 0.0825t2 = 0 Solving 1.752 + -0.886t + 0.0825t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 0.0825 the coefficient of the squared term: Divide each side by '0.0825'. 21.23636364 + -10.73939394t + t2 = 0 Move the constant term to the right: Add '-21.23636364' to each side of the equation. 21.23636364 + -10.73939394t + -21.23636364 + t2 = 0 + -21.23636364 Reorder the terms: 21.23636364 + -21.23636364 + -10.73939394t + t2 = 0 + -21.23636364 Combine like terms: 21.23636364 + -21.23636364 = 0.00000000 0.00000000 + -10.73939394t + t2 = 0 + -21.23636364 -10.73939394t + t2 = 0 + -21.23636364 Combine like terms: 0 + -21.23636364 = -21.23636364 -10.73939394t + t2 = -21.23636364 The t term is -10.73939394t. Take half its coefficient (-5.36969697). Square it (28.83364555) and add it to both sides. Add '28.83364555' to each side of the equation. -10.73939394t + 28.83364555 + t2 = -21.23636364 + 28.83364555 Reorder the terms: 28.83364555 + -10.73939394t + t2 = -21.23636364 + 28.83364555 Combine like terms: -21.23636364 + 28.83364555 = 7.59728191 28.83364555 + -10.73939394t + t2 = 7.59728191 Factor a perfect square on the left side: (t + -5.36969697)(t + -5.36969697) = 7.59728191 Calculate the square root of the right side: 2.756316729 Break this problem into two subproblems by setting (t + -5.36969697) equal to 2.756316729 and -2.756316729.Subproblem 1
t + -5.36969697 = 2.756316729 Simplifying t + -5.36969697 = 2.756316729 Reorder the terms: -5.36969697 + t = 2.756316729 Solving -5.36969697 + t = 2.756316729 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.36969697' to each side of the equation. -5.36969697 + 5.36969697 + t = 2.756316729 + 5.36969697 Combine like terms: -5.36969697 + 5.36969697 = 0.00000000 0.00000000 + t = 2.756316729 + 5.36969697 t = 2.756316729 + 5.36969697 Combine like terms: 2.756316729 + 5.36969697 = 8.126013699 t = 8.126013699 Simplifying t = 8.126013699Subproblem 2
t + -5.36969697 = -2.756316729 Simplifying t + -5.36969697 = -2.756316729 Reorder the terms: -5.36969697 + t = -2.756316729 Solving -5.36969697 + t = -2.756316729 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.36969697' to each side of the equation. -5.36969697 + 5.36969697 + t = -2.756316729 + 5.36969697 Combine like terms: -5.36969697 + 5.36969697 = 0.00000000 0.00000000 + t = -2.756316729 + 5.36969697 t = -2.756316729 + 5.36969697 Combine like terms: -2.756316729 + 5.36969697 = 2.613380241 t = 2.613380241 Simplifying t = 2.613380241Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.126013699, 2.613380241}
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