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Simplifying 0.0915t2 + -0.926t + 1.747 = 0 Reorder the terms: 1.747 + -0.926t + 0.0915t2 = 0 Solving 1.747 + -0.926t + 0.0915t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 0.0915 the coefficient of the squared term: Divide each side by '0.0915'. 19.09289617 + -10.12021858t + t2 = 0 Move the constant term to the right: Add '-19.09289617' to each side of the equation. 19.09289617 + -10.12021858t + -19.09289617 + t2 = 0 + -19.09289617 Reorder the terms: 19.09289617 + -19.09289617 + -10.12021858t + t2 = 0 + -19.09289617 Combine like terms: 19.09289617 + -19.09289617 = 0.00000000 0.00000000 + -10.12021858t + t2 = 0 + -19.09289617 -10.12021858t + t2 = 0 + -19.09289617 Combine like terms: 0 + -19.09289617 = -19.09289617 -10.12021858t + t2 = -19.09289617 The t term is -10.12021858t. Take half its coefficient (-5.06010929). Square it (25.60470603) and add it to both sides. Add '25.60470603' to each side of the equation. -10.12021858t + 25.60470603 + t2 = -19.09289617 + 25.60470603 Reorder the terms: 25.60470603 + -10.12021858t + t2 = -19.09289617 + 25.60470603 Combine like terms: -19.09289617 + 25.60470603 = 6.51180986 25.60470603 + -10.12021858t + t2 = 6.51180986 Factor a perfect square on the left side: (t + -5.06010929)(t + -5.06010929) = 6.51180986 Calculate the square root of the right side: 2.55182481 Break this problem into two subproblems by setting (t + -5.06010929) equal to 2.55182481 and -2.55182481.Subproblem 1
t + -5.06010929 = 2.55182481 Simplifying t + -5.06010929 = 2.55182481 Reorder the terms: -5.06010929 + t = 2.55182481 Solving -5.06010929 + t = 2.55182481 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.06010929' to each side of the equation. -5.06010929 + 5.06010929 + t = 2.55182481 + 5.06010929 Combine like terms: -5.06010929 + 5.06010929 = 0.00000000 0.00000000 + t = 2.55182481 + 5.06010929 t = 2.55182481 + 5.06010929 Combine like terms: 2.55182481 + 5.06010929 = 7.6119341 t = 7.6119341 Simplifying t = 7.6119341Subproblem 2
t + -5.06010929 = -2.55182481 Simplifying t + -5.06010929 = -2.55182481 Reorder the terms: -5.06010929 + t = -2.55182481 Solving -5.06010929 + t = -2.55182481 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.06010929' to each side of the equation. -5.06010929 + 5.06010929 + t = -2.55182481 + 5.06010929 Combine like terms: -5.06010929 + 5.06010929 = 0.00000000 0.00000000 + t = -2.55182481 + 5.06010929 t = -2.55182481 + 5.06010929 Combine like terms: -2.55182481 + 5.06010929 = 2.50828448 t = 2.50828448 Simplifying t = 2.50828448Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.6119341, 2.50828448}
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