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Simplifying 16 = 2 + 33t + -16t2 Solving 16 = 2 + 33t + -16t2 Solving for variable 't'. Combine like terms: 16 + -2 = 14 14 + -33t + 16t2 = 2 + 33t + -16t2 + -2 + -33t + 16t2 Reorder the terms: 14 + -33t + 16t2 = 2 + -2 + 33t + -33t + -16t2 + 16t2 Combine like terms: 2 + -2 = 0 14 + -33t + 16t2 = 0 + 33t + -33t + -16t2 + 16t2 14 + -33t + 16t2 = 33t + -33t + -16t2 + 16t2 Combine like terms: 33t + -33t = 0 14 + -33t + 16t2 = 0 + -16t2 + 16t2 14 + -33t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 14 + -33t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.875 + -2.0625t + t2 = 0 Move the constant term to the right: Add '-0.875' to each side of the equation. 0.875 + -2.0625t + -0.875 + t2 = 0 + -0.875 Reorder the terms: 0.875 + -0.875 + -2.0625t + t2 = 0 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + -2.0625t + t2 = 0 + -0.875 -2.0625t + t2 = 0 + -0.875 Combine like terms: 0 + -0.875 = -0.875 -2.0625t + t2 = -0.875 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 = -0.875 + 1.063476563 Reorder the terms: 1.063476563 + -2.0625t + t2 = -0.875 + 1.063476563 Combine like terms: -0.875 + 1.063476563 = 0.188476563 1.063476563 + -2.0625t + t2 = 0.188476563 Factor a perfect square on the left side: (t + -1.03125)(t + -1.03125) = 0.188476563 Calculate the square root of the right side: 0.434138875 Break this problem into two subproblems by setting (t + -1.03125) equal to 0.434138875 and -0.434138875.Subproblem 1
t + -1.03125 = 0.434138875 Simplifying t + -1.03125 = 0.434138875 Reorder the terms: -1.03125 + t = 0.434138875 Solving -1.03125 + t = 0.434138875 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 = 0.434138875 + 1.03125 Combine like terms: -1.03125 + 1.03125 = 0.00000 0.00000 + t = 0.434138875 + 1.03125 t = 0.434138875 + 1.03125 Combine like terms: 0.434138875 + 1.03125 = 1.465388875 t = 1.465388875 Simplifying t = 1.465388875Subproblem 2
t + -1.03125 = -0.434138875 Simplifying t + -1.03125 = -0.434138875 Reorder the terms: -1.03125 + t = -0.434138875 Solving -1.03125 + t = -0.434138875 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 = -0.434138875 + 1.03125 Combine like terms: -1.03125 + 1.03125 = 0.00000 0.00000 + t = -0.434138875 + 1.03125 t = -0.434138875 + 1.03125 Combine like terms: -0.434138875 + 1.03125 = 0.597111125 t = 0.597111125 Simplifying t = 0.597111125Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.465388875, 0.597111125}
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