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Simplifying 0 = -16t2 + -25t + 150 Reorder the terms: 0 = 150 + -25t + -16t2 Solving 0 = 150 + -25t + -16t2 Solving for variable 't'. Combine like terms: 0 + -150 = -150 -150 + 25t + 16t2 = 150 + -25t + -16t2 + -150 + 25t + 16t2 Reorder the terms: -150 + 25t + 16t2 = 150 + -150 + -25t + 25t + -16t2 + 16t2 Combine like terms: 150 + -150 = 0 -150 + 25t + 16t2 = 0 + -25t + 25t + -16t2 + 16t2 -150 + 25t + 16t2 = -25t + 25t + -16t2 + 16t2 Combine like terms: -25t + 25t = 0 -150 + 25t + 16t2 = 0 + -16t2 + 16t2 -150 + 25t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -150 + 25t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -9.375 + 1.5625t + t2 = 0 Move the constant term to the right: Add '9.375' to each side of the equation. -9.375 + 1.5625t + 9.375 + t2 = 0 + 9.375 Reorder the terms: -9.375 + 9.375 + 1.5625t + t2 = 0 + 9.375 Combine like terms: -9.375 + 9.375 = 0.000 0.000 + 1.5625t + t2 = 0 + 9.375 1.5625t + t2 = 0 + 9.375 Combine like terms: 0 + 9.375 = 9.375 1.5625t + t2 = 9.375 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 = 9.375 + 0.6103515625 Reorder the terms: 0.6103515625 + 1.5625t + t2 = 9.375 + 0.6103515625 Combine like terms: 9.375 + 0.6103515625 = 9.9853515625 0.6103515625 + 1.5625t + t2 = 9.9853515625 Factor a perfect square on the left side: (t + 0.78125)(t + 0.78125) = 9.9853515625 Calculate the square root of the right side: 3.15996069 Break this problem into two subproblems by setting (t + 0.78125) equal to 3.15996069 and -3.15996069.Subproblem 1
t + 0.78125 = 3.15996069 Simplifying t + 0.78125 = 3.15996069 Reorder the terms: 0.78125 + t = 3.15996069 Solving 0.78125 + t = 3.15996069 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 = 3.15996069 + -0.78125 Combine like terms: 0.78125 + -0.78125 = 0.00000 0.00000 + t = 3.15996069 + -0.78125 t = 3.15996069 + -0.78125 Combine like terms: 3.15996069 + -0.78125 = 2.37871069 t = 2.37871069 Simplifying t = 2.37871069Subproblem 2
t + 0.78125 = -3.15996069 Simplifying t + 0.78125 = -3.15996069 Reorder the terms: 0.78125 + t = -3.15996069 Solving 0.78125 + t = -3.15996069 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 = -3.15996069 + -0.78125 Combine like terms: 0.78125 + -0.78125 = 0.00000 0.00000 + t = -3.15996069 + -0.78125 t = -3.15996069 + -0.78125 Combine like terms: -3.15996069 + -0.78125 = -3.94121069 t = -3.94121069 Simplifying t = -3.94121069Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.37871069, -3.94121069}
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