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Simplifying 9 = 5 + 17t + -16t2 Solving 9 = 5 + 17t + -16t2 Solving for variable 't'. Combine like terms: 9 + -5 = 4 4 + -17t + 16t2 = 5 + 17t + -16t2 + -5 + -17t + 16t2 Reorder the terms: 4 + -17t + 16t2 = 5 + -5 + 17t + -17t + -16t2 + 16t2 Combine like terms: 5 + -5 = 0 4 + -17t + 16t2 = 0 + 17t + -17t + -16t2 + 16t2 4 + -17t + 16t2 = 17t + -17t + -16t2 + 16t2 Combine like terms: 17t + -17t = 0 4 + -17t + 16t2 = 0 + -16t2 + 16t2 4 + -17t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 4 + -17t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.25 + -1.0625t + t2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + -1.0625t + -0.25 + t2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + -1.0625t + t2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + -1.0625t + t2 = 0 + -0.25 -1.0625t + t2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 -1.0625t + t2 = -0.25 The t term is -1.0625t. Take half its coefficient (-0.53125). Square it (0.2822265625) and add it to both sides. Add '0.2822265625' to each side of the equation. -1.0625t + 0.2822265625 + t2 = -0.25 + 0.2822265625 Reorder the terms: 0.2822265625 + -1.0625t + t2 = -0.25 + 0.2822265625 Combine like terms: -0.25 + 0.2822265625 = 0.0322265625 0.2822265625 + -1.0625t + t2 = 0.0322265625 Factor a perfect square on the left side: (t + -0.53125)(t + -0.53125) = 0.0322265625 Calculate the square root of the right side: 0.179517583 Break this problem into two subproblems by setting (t + -0.53125) equal to 0.179517583 and -0.179517583.Subproblem 1
t + -0.53125 = 0.179517583 Simplifying t + -0.53125 = 0.179517583 Reorder the terms: -0.53125 + t = 0.179517583 Solving -0.53125 + t = 0.179517583 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.53125' to each side of the equation. -0.53125 + 0.53125 + t = 0.179517583 + 0.53125 Combine like terms: -0.53125 + 0.53125 = 0.00000 0.00000 + t = 0.179517583 + 0.53125 t = 0.179517583 + 0.53125 Combine like terms: 0.179517583 + 0.53125 = 0.710767583 t = 0.710767583 Simplifying t = 0.710767583Subproblem 2
t + -0.53125 = -0.179517583 Simplifying t + -0.53125 = -0.179517583 Reorder the terms: -0.53125 + t = -0.179517583 Solving -0.53125 + t = -0.179517583 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.53125' to each side of the equation. -0.53125 + 0.53125 + t = -0.179517583 + 0.53125 Combine like terms: -0.53125 + 0.53125 = 0.00000 0.00000 + t = -0.179517583 + 0.53125 t = -0.179517583 + 0.53125 Combine like terms: -0.179517583 + 0.53125 = 0.351732417 t = 0.351732417 Simplifying t = 0.351732417Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.710767583, 0.351732417}
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