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Simplifying 16t2 + -33t = -16 Reorder the terms: -33t + 16t2 = -16 Solving -33t + 16t2 = -16 Solving for variable 't'. Reorder the terms: 16 + -33t + 16t2 = -16 + 16 Combine like terms: -16 + 16 = 0 16 + -33t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 1 + -2.0625t + t2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -2.0625t + -1 + t2 = 0 + -1 Reorder the terms: 1 + -1 + -2.0625t + t2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2.0625t + t2 = 0 + -1 -2.0625t + t2 = 0 + -1 Combine like terms: 0 + -1 = -1 -2.0625t + t2 = -1 The t term is -2.0625t. Take half its coefficient (-1.03125). Square it (1.063476563) and add it to both sides. Add '1.063476563' to each side of the equation. -2.0625t + 1.063476563 + t2 = -1 + 1.063476563 Reorder the terms: 1.063476563 + -2.0625t + t2 = -1 + 1.063476563 Combine like terms: -1 + 1.063476563 = 0.063476563 1.063476563 + -2.0625t + t2 = 0.063476563 Factor a perfect square on the left side: (t + -1.03125)(t + -1.03125) = 0.063476563 Calculate the square root of the right side: 0.251945556 Break this problem into two subproblems by setting (t + -1.03125) equal to 0.251945556 and -0.251945556.Subproblem 1
t + -1.03125 = 0.251945556 Simplifying t + -1.03125 = 0.251945556 Reorder the terms: -1.03125 + t = 0.251945556 Solving -1.03125 + t = 0.251945556 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.03125' to each side of the equation. -1.03125 + 1.03125 + t = 0.251945556 + 1.03125 Combine like terms: -1.03125 + 1.03125 = 0.00000 0.00000 + t = 0.251945556 + 1.03125 t = 0.251945556 + 1.03125 Combine like terms: 0.251945556 + 1.03125 = 1.283195556 t = 1.283195556 Simplifying t = 1.283195556Subproblem 2
t + -1.03125 = -0.251945556 Simplifying t + -1.03125 = -0.251945556 Reorder the terms: -1.03125 + t = -0.251945556 Solving -1.03125 + t = -0.251945556 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.03125' to each side of the equation. -1.03125 + 1.03125 + t = -0.251945556 + 1.03125 Combine like terms: -1.03125 + 1.03125 = 0.00000 0.00000 + t = -0.251945556 + 1.03125 t = -0.251945556 + 1.03125 Combine like terms: -0.251945556 + 1.03125 = 0.779304444 t = 0.779304444 Simplifying t = 0.779304444Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.283195556, 0.779304444}
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