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Simplifying 0 = (-16t2) + 97t + 556 Reorder the terms: 0 = 556 + 97t + (-16t2) Solving 0 = 556 + 97t + (-16t2) Solving for variable 't'. Combine like terms: 0 + -556 = -556 -556 + -97t + (16t2) = 556 + 97t + (-16t2) + -556 + -97t + (16t2) Reorder the terms: -556 + -97t + (16t2) = 556 + -556 + 97t + -97t + (-16t2) + (16t2) Combine like terms: 556 + -556 = 0 -556 + -97t + (16t2) = 0 + 97t + -97t + (-16t2) + (16t2) -556 + -97t + (16t2) = 97t + -97t + (-16t2) + (16t2) Combine like terms: 97t + -97t = 0 -556 + -97t + (16t2) = 0 + (-16t2) + (16t2) -556 + -97t + (16t2) = (-16t2) + (16t2) Combine like terms: (-16t2) + (16t2) = 0 -556 + -97t + (16t2) = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -34.75 + -6.0625t + t2 = 0 Move the constant term to the right: Add '34.75' to each side of the equation. -34.75 + -6.0625t + 34.75 + t2 = 0 + 34.75 Reorder the terms: -34.75 + 34.75 + -6.0625t + t2 = 0 + 34.75 Combine like terms: -34.75 + 34.75 = 0.00 0.00 + -6.0625t + t2 = 0 + 34.75 -6.0625t + t2 = 0 + 34.75 Combine like terms: 0 + 34.75 = 34.75 -6.0625t + t2 = 34.75 The t term is -6.0625t. Take half its coefficient (-3.03125). Square it (9.188476563) and add it to both sides. Add '9.188476563' to each side of the equation. -6.0625t + 9.188476563 + t2 = 34.75 + 9.188476563 Reorder the terms: 9.188476563 + -6.0625t + t2 = 34.75 + 9.188476563 Combine like terms: 34.75 + 9.188476563 = 43.938476563 9.188476563 + -6.0625t + t2 = 43.938476563 Factor a perfect square on the left side: ((t) + -3.03125)((t) + -3.03125) = 43.938476563 Calculate the square root of the right side: 6.628610455 Break this problem into two subproblems by setting ((t) + -3.03125) equal to 6.628610455 and -6.628610455.Subproblem 1
(t) + -3.03125 = 6.628610455 Simplifying (t) + -3.03125 = 6.628610455 t + -3.03125 = 6.628610455 Reorder the terms: -3.03125 + t = 6.628610455 Solving -3.03125 + t = 6.628610455 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.03125' to each side of the equation. -3.03125 + 3.03125 + t = 6.628610455 + 3.03125 Combine like terms: -3.03125 + 3.03125 = 0.00000 0.00000 + t = 6.628610455 + 3.03125 t = 6.628610455 + 3.03125 Combine like terms: 6.628610455 + 3.03125 = 9.659860455 t = 9.659860455 Simplifying t = 9.659860455Subproblem 2
(t) + -3.03125 = -6.628610455 Simplifying (t) + -3.03125 = -6.628610455 t + -3.03125 = -6.628610455 Reorder the terms: -3.03125 + t = -6.628610455 Solving -3.03125 + t = -6.628610455 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.03125' to each side of the equation. -3.03125 + 3.03125 + t = -6.628610455 + 3.03125 Combine like terms: -3.03125 + 3.03125 = 0.00000 0.00000 + t = -6.628610455 + 3.03125 t = -6.628610455 + 3.03125 Combine like terms: -6.628610455 + 3.03125 = -3.597360455 t = -3.597360455 Simplifying t = -3.597360455Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.659860455, -3.597360455}
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