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Simplifying 0.0915t2 + -0.926t + 1.743 = 0 Reorder the terms: 1.743 + -0.926t + 0.0915t2 = 0 Solving 1.743 + -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'. 19.04918033 + -10.12021858t + t2 = 0 Move the constant term to the right: Add '-19.04918033' to each side of the equation. 19.04918033 + -10.12021858t + -19.04918033 + t2 = 0 + -19.04918033 Reorder the terms: 19.04918033 + -19.04918033 + -10.12021858t + t2 = 0 + -19.04918033 Combine like terms: 19.04918033 + -19.04918033 = 0.00000000 0.00000000 + -10.12021858t + t2 = 0 + -19.04918033 -10.12021858t + t2 = 0 + -19.04918033 Combine like terms: 0 + -19.04918033 = -19.04918033 -10.12021858t + t2 = -19.04918033 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 = -19.04918033 + 25.60470603 Reorder the terms: 25.60470603 + -10.12021858t + t2 = -19.04918033 + 25.60470603 Combine like terms: -19.04918033 + 25.60470603 = 6.5555257 25.60470603 + -10.12021858t + t2 = 6.5555257 Factor a perfect square on the left side: (t + -5.06010929)(t + -5.06010929) = 6.5555257 Calculate the square root of the right side: 2.560376086 Break this problem into two subproblems by setting (t + -5.06010929) equal to 2.560376086 and -2.560376086.Subproblem 1
t + -5.06010929 = 2.560376086 Simplifying t + -5.06010929 = 2.560376086 Reorder the terms: -5.06010929 + t = 2.560376086 Solving -5.06010929 + t = 2.560376086 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 = 2.560376086 + 5.06010929 Combine like terms: -5.06010929 + 5.06010929 = 0.00000000 0.00000000 + t = 2.560376086 + 5.06010929 t = 2.560376086 + 5.06010929 Combine like terms: 2.560376086 + 5.06010929 = 7.620485376 t = 7.620485376 Simplifying t = 7.620485376Subproblem 2
t + -5.06010929 = -2.560376086 Simplifying t + -5.06010929 = -2.560376086 Reorder the terms: -5.06010929 + t = -2.560376086 Solving -5.06010929 + t = -2.560376086 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 = -2.560376086 + 5.06010929 Combine like terms: -5.06010929 + 5.06010929 = 0.00000000 0.00000000 + t = -2.560376086 + 5.06010929 t = -2.560376086 + 5.06010929 Combine like terms: -2.560376086 + 5.06010929 = 2.499733204 t = 2.499733204 Simplifying t = 2.499733204Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.620485376, 2.499733204}
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