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Simplifying 16t2 + -110t + 185 = 0 Reorder the terms: 185 + -110t + 16t2 = 0 Solving 185 + -110t + 16t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 11.5625 + -6.875t + t2 = 0 Move the constant term to the right: Add '-11.5625' to each side of the equation. 11.5625 + -6.875t + -11.5625 + t2 = 0 + -11.5625 Reorder the terms: 11.5625 + -11.5625 + -6.875t + t2 = 0 + -11.5625 Combine like terms: 11.5625 + -11.5625 = 0.0000 0.0000 + -6.875t + t2 = 0 + -11.5625 -6.875t + t2 = 0 + -11.5625 Combine like terms: 0 + -11.5625 = -11.5625 -6.875t + t2 = -11.5625 The t term is -6.875t. Take half its coefficient (-3.4375). Square it (11.81640625) and add it to both sides. Add '11.81640625' to each side of the equation. -6.875t + 11.81640625 + t2 = -11.5625 + 11.81640625 Reorder the terms: 11.81640625 + -6.875t + t2 = -11.5625 + 11.81640625 Combine like terms: -11.5625 + 11.81640625 = 0.25390625 11.81640625 + -6.875t + t2 = 0.25390625 Factor a perfect square on the left side: (t + -3.4375)(t + -3.4375) = 0.25390625 Calculate the square root of the right side: 0.503891109 Break this problem into two subproblems by setting (t + -3.4375) equal to 0.503891109 and -0.503891109.Subproblem 1
t + -3.4375 = 0.503891109 Simplifying t + -3.4375 = 0.503891109 Reorder the terms: -3.4375 + t = 0.503891109 Solving -3.4375 + t = 0.503891109 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.4375' to each side of the equation. -3.4375 + 3.4375 + t = 0.503891109 + 3.4375 Combine like terms: -3.4375 + 3.4375 = 0.0000 0.0000 + t = 0.503891109 + 3.4375 t = 0.503891109 + 3.4375 Combine like terms: 0.503891109 + 3.4375 = 3.941391109 t = 3.941391109 Simplifying t = 3.941391109Subproblem 2
t + -3.4375 = -0.503891109 Simplifying t + -3.4375 = -0.503891109 Reorder the terms: -3.4375 + t = -0.503891109 Solving -3.4375 + t = -0.503891109 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.4375' to each side of the equation. -3.4375 + 3.4375 + t = -0.503891109 + 3.4375 Combine like terms: -3.4375 + 3.4375 = 0.0000 0.0000 + t = -0.503891109 + 3.4375 t = -0.503891109 + 3.4375 Combine like terms: -0.503891109 + 3.4375 = 2.933608891 t = 2.933608891 Simplifying t = 2.933608891Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.941391109, 2.933608891}
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