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Simplifying 0 = -16t2 + 110t + 165 Reorder the terms: 0 = 165 + 110t + -16t2 Solving 0 = 165 + 110t + -16t2 Solving for variable 't'. Combine like terms: 0 + -165 = -165 -165 + -110t + 16t2 = 165 + 110t + -16t2 + -165 + -110t + 16t2 Reorder the terms: -165 + -110t + 16t2 = 165 + -165 + 110t + -110t + -16t2 + 16t2 Combine like terms: 165 + -165 = 0 -165 + -110t + 16t2 = 0 + 110t + -110t + -16t2 + 16t2 -165 + -110t + 16t2 = 110t + -110t + -16t2 + 16t2 Combine like terms: 110t + -110t = 0 -165 + -110t + 16t2 = 0 + -16t2 + 16t2 -165 + -110t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -165 + -110t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -10.3125 + -6.875t + t2 = 0 Move the constant term to the right: Add '10.3125' to each side of the equation. -10.3125 + -6.875t + 10.3125 + t2 = 0 + 10.3125 Reorder the terms: -10.3125 + 10.3125 + -6.875t + t2 = 0 + 10.3125 Combine like terms: -10.3125 + 10.3125 = 0.0000 0.0000 + -6.875t + t2 = 0 + 10.3125 -6.875t + t2 = 0 + 10.3125 Combine like terms: 0 + 10.3125 = 10.3125 -6.875t + t2 = 10.3125 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 = 10.3125 + 11.81640625 Reorder the terms: 11.81640625 + -6.875t + t2 = 10.3125 + 11.81640625 Combine like terms: 10.3125 + 11.81640625 = 22.12890625 11.81640625 + -6.875t + t2 = 22.12890625 Factor a perfect square on the left side: (t + -3.4375)(t + -3.4375) = 22.12890625 Calculate the square root of the right side: 4.704137142 Break this problem into two subproblems by setting (t + -3.4375) equal to 4.704137142 and -4.704137142.Subproblem 1
t + -3.4375 = 4.704137142 Simplifying t + -3.4375 = 4.704137142 Reorder the terms: -3.4375 + t = 4.704137142 Solving -3.4375 + t = 4.704137142 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 = 4.704137142 + 3.4375 Combine like terms: -3.4375 + 3.4375 = 0.0000 0.0000 + t = 4.704137142 + 3.4375 t = 4.704137142 + 3.4375 Combine like terms: 4.704137142 + 3.4375 = 8.141637142 t = 8.141637142 Simplifying t = 8.141637142Subproblem 2
t + -3.4375 = -4.704137142 Simplifying t + -3.4375 = -4.704137142 Reorder the terms: -3.4375 + t = -4.704137142 Solving -3.4375 + t = -4.704137142 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 = -4.704137142 + 3.4375 Combine like terms: -3.4375 + 3.4375 = 0.0000 0.0000 + t = -4.704137142 + 3.4375 t = -4.704137142 + 3.4375 Combine like terms: -4.704137142 + 3.4375 = -1.266637142 t = -1.266637142 Simplifying t = -1.266637142Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.141637142, -1.266637142}
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