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Simplifying t = -16t2 + 576 Reorder the terms: t = 576 + -16t2 Solving t = 576 + -16t2 Solving for variable 't'. Reorder the terms: -576 + t + 16t2 = 576 + -16t2 + -576 + 16t2 Reorder the terms: -576 + t + 16t2 = 576 + -576 + -16t2 + 16t2 Combine like terms: 576 + -576 = 0 -576 + t + 16t2 = 0 + -16t2 + 16t2 -576 + t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -576 + t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -36 + 0.0625t + t2 = 0 Move the constant term to the right: Add '36' to each side of the equation. -36 + 0.0625t + 36 + t2 = 0 + 36 Reorder the terms: -36 + 36 + 0.0625t + t2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + 0.0625t + t2 = 0 + 36 0.0625t + t2 = 0 + 36 Combine like terms: 0 + 36 = 36 0.0625t + t2 = 36 The t term is t. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.0625t + 0.25 + t2 = 36 + 0.25 Reorder the terms: 0.25 + 0.0625t + t2 = 36 + 0.25 Combine like terms: 36 + 0.25 = 36.25 0.25 + 0.0625t + t2 = 36.25 Factor a perfect square on the left side: (t + 0.5)(t + 0.5) = 36.25 Calculate the square root of the right side: 6.020797289 Break this problem into two subproblems by setting (t + 0.5) equal to 6.020797289 and -6.020797289.Subproblem 1
t + 0.5 = 6.020797289 Simplifying t + 0.5 = 6.020797289 Reorder the terms: 0.5 + t = 6.020797289 Solving 0.5 + t = 6.020797289 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = 6.020797289 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = 6.020797289 + -0.5 t = 6.020797289 + -0.5 Combine like terms: 6.020797289 + -0.5 = 5.520797289 t = 5.520797289 Simplifying t = 5.520797289Subproblem 2
t + 0.5 = -6.020797289 Simplifying t + 0.5 = -6.020797289 Reorder the terms: 0.5 + t = -6.020797289 Solving 0.5 + t = -6.020797289 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = -6.020797289 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = -6.020797289 + -0.5 t = -6.020797289 + -0.5 Combine like terms: -6.020797289 + -0.5 = -6.520797289 t = -6.520797289 Simplifying t = -6.520797289Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.520797289, -6.520797289}
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