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Simplifying 4 = -16t2 + 25t Reorder the terms: 4 = 25t + -16t2 Solving 4 = 25t + -16t2 Solving for variable 't'. Reorder the terms: 4 + -25t + 16t2 = 25t + -25t + -16t2 + 16t2 Combine like terms: 25t + -25t = 0 4 + -25t + 16t2 = 0 + -16t2 + 16t2 4 + -25t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 4 + -25t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.25 + -1.5625t + t2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + -1.5625t + -0.25 + t2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + -1.5625t + t2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + -1.5625t + t2 = 0 + -0.25 -1.5625t + t2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 -1.5625t + t2 = -0.25 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 = -0.25 + 0.6103515625 Reorder the terms: 0.6103515625 + -1.5625t + t2 = -0.25 + 0.6103515625 Combine like terms: -0.25 + 0.6103515625 = 0.3603515625 0.6103515625 + -1.5625t + t2 = 0.3603515625 Factor a perfect square on the left side: (t + -0.78125)(t + -0.78125) = 0.3603515625 Calculate the square root of the right side: 0.600292897 Break this problem into two subproblems by setting (t + -0.78125) equal to 0.600292897 and -0.600292897.Subproblem 1
t + -0.78125 = 0.600292897 Simplifying t + -0.78125 = 0.600292897 Reorder the terms: -0.78125 + t = 0.600292897 Solving -0.78125 + t = 0.600292897 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 = 0.600292897 + 0.78125 Combine like terms: -0.78125 + 0.78125 = 0.00000 0.00000 + t = 0.600292897 + 0.78125 t = 0.600292897 + 0.78125 Combine like terms: 0.600292897 + 0.78125 = 1.381542897 t = 1.381542897 Simplifying t = 1.381542897Subproblem 2
t + -0.78125 = -0.600292897 Simplifying t + -0.78125 = -0.600292897 Reorder the terms: -0.78125 + t = -0.600292897 Solving -0.78125 + t = -0.600292897 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 = -0.600292897 + 0.78125 Combine like terms: -0.78125 + 0.78125 = 0.00000 0.00000 + t = -0.600292897 + 0.78125 t = -0.600292897 + 0.78125 Combine like terms: -0.600292897 + 0.78125 = 0.180957103 t = 0.180957103 Simplifying t = 0.180957103Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.381542897, 0.180957103}
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