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Simplifying 16t2 + -195t + 87 = 0 Reorder the terms: 87 + -195t + 16t2 = 0 Solving 87 + -195t + 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'. 5.4375 + -12.1875t + t2 = 0 Move the constant term to the right: Add '-5.4375' to each side of the equation. 5.4375 + -12.1875t + -5.4375 + t2 = 0 + -5.4375 Reorder the terms: 5.4375 + -5.4375 + -12.1875t + t2 = 0 + -5.4375 Combine like terms: 5.4375 + -5.4375 = 0.0000 0.0000 + -12.1875t + t2 = 0 + -5.4375 -12.1875t + t2 = 0 + -5.4375 Combine like terms: 0 + -5.4375 = -5.4375 -12.1875t + t2 = -5.4375 The t term is -12.1875t. Take half its coefficient (-6.09375). Square it (37.13378906) and add it to both sides. Add '37.13378906' to each side of the equation. -12.1875t + 37.13378906 + t2 = -5.4375 + 37.13378906 Reorder the terms: 37.13378906 + -12.1875t + t2 = -5.4375 + 37.13378906 Combine like terms: -5.4375 + 37.13378906 = 31.69628906 37.13378906 + -12.1875t + t2 = 31.69628906 Factor a perfect square on the left side: (t + -6.09375)(t + -6.09375) = 31.69628906 Calculate the square root of the right side: 5.629945742 Break this problem into two subproblems by setting (t + -6.09375) equal to 5.629945742 and -5.629945742.Subproblem 1
t + -6.09375 = 5.629945742 Simplifying t + -6.09375 = 5.629945742 Reorder the terms: -6.09375 + t = 5.629945742 Solving -6.09375 + t = 5.629945742 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.09375' to each side of the equation. -6.09375 + 6.09375 + t = 5.629945742 + 6.09375 Combine like terms: -6.09375 + 6.09375 = 0.00000 0.00000 + t = 5.629945742 + 6.09375 t = 5.629945742 + 6.09375 Combine like terms: 5.629945742 + 6.09375 = 11.723695742 t = 11.723695742 Simplifying t = 11.723695742Subproblem 2
t + -6.09375 = -5.629945742 Simplifying t + -6.09375 = -5.629945742 Reorder the terms: -6.09375 + t = -5.629945742 Solving -6.09375 + t = -5.629945742 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.09375' to each side of the equation. -6.09375 + 6.09375 + t = -5.629945742 + 6.09375 Combine like terms: -6.09375 + 6.09375 = 0.00000 0.00000 + t = -5.629945742 + 6.09375 t = -5.629945742 + 6.09375 Combine like terms: -5.629945742 + 6.09375 = 0.463804258 t = 0.463804258 Simplifying t = 0.463804258Solution
The solution to the problem is based on the solutions from the subproblems. t = {11.723695742, 0.463804258}
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