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Simplifying 0 = -16t2 + -25t + 260 Reorder the terms: 0 = 260 + -25t + -16t2 Solving 0 = 260 + -25t + -16t2 Solving for variable 't'. Combine like terms: 0 + -260 = -260 -260 + 25t + 16t2 = 260 + -25t + -16t2 + -260 + 25t + 16t2 Reorder the terms: -260 + 25t + 16t2 = 260 + -260 + -25t + 25t + -16t2 + 16t2 Combine like terms: 260 + -260 = 0 -260 + 25t + 16t2 = 0 + -25t + 25t + -16t2 + 16t2 -260 + 25t + 16t2 = -25t + 25t + -16t2 + 16t2 Combine like terms: -25t + 25t = 0 -260 + 25t + 16t2 = 0 + -16t2 + 16t2 -260 + 25t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -260 + 25t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -16.25 + 1.5625t + t2 = 0 Move the constant term to the right: Add '16.25' to each side of the equation. -16.25 + 1.5625t + 16.25 + t2 = 0 + 16.25 Reorder the terms: -16.25 + 16.25 + 1.5625t + t2 = 0 + 16.25 Combine like terms: -16.25 + 16.25 = 0.00 0.00 + 1.5625t + t2 = 0 + 16.25 1.5625t + t2 = 0 + 16.25 Combine like terms: 0 + 16.25 = 16.25 1.5625t + t2 = 16.25 The t term is 1.5625t. Take half its coefficient (0.78125). Square it (0.6103515625) and add it to both sides. Add '0.6103515625' to each side of the equation. 1.5625t + 0.6103515625 + t2 = 16.25 + 0.6103515625 Reorder the terms: 0.6103515625 + 1.5625t + t2 = 16.25 + 0.6103515625 Combine like terms: 16.25 + 0.6103515625 = 16.8603515625 0.6103515625 + 1.5625t + t2 = 16.8603515625 Factor a perfect square on the left side: (t + 0.78125)(t + 0.78125) = 16.8603515625 Calculate the square root of the right side: 4.106135843 Break this problem into two subproblems by setting (t + 0.78125) equal to 4.106135843 and -4.106135843.Subproblem 1
t + 0.78125 = 4.106135843 Simplifying t + 0.78125 = 4.106135843 Reorder the terms: 0.78125 + t = 4.106135843 Solving 0.78125 + t = 4.106135843 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.78125' to each side of the equation. 0.78125 + -0.78125 + t = 4.106135843 + -0.78125 Combine like terms: 0.78125 + -0.78125 = 0.00000 0.00000 + t = 4.106135843 + -0.78125 t = 4.106135843 + -0.78125 Combine like terms: 4.106135843 + -0.78125 = 3.324885843 t = 3.324885843 Simplifying t = 3.324885843Subproblem 2
t + 0.78125 = -4.106135843 Simplifying t + 0.78125 = -4.106135843 Reorder the terms: 0.78125 + t = -4.106135843 Solving 0.78125 + t = -4.106135843 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.78125' to each side of the equation. 0.78125 + -0.78125 + t = -4.106135843 + -0.78125 Combine like terms: 0.78125 + -0.78125 = 0.00000 0.00000 + t = -4.106135843 + -0.78125 t = -4.106135843 + -0.78125 Combine like terms: -4.106135843 + -0.78125 = -4.887385843 t = -4.887385843 Simplifying t = -4.887385843Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.324885843, -4.887385843}
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