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Simplifying 16t2 + -17t + -217 = 0 Reorder the terms: -217 + -17t + 16t2 = 0 Solving -217 + -17t + 16t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -13.5625 + -1.0625t + t2 = 0 Move the constant term to the right: Add '13.5625' to each side of the equation. -13.5625 + -1.0625t + 13.5625 + t2 = 0 + 13.5625 Reorder the terms: -13.5625 + 13.5625 + -1.0625t + t2 = 0 + 13.5625 Combine like terms: -13.5625 + 13.5625 = 0.0000 0.0000 + -1.0625t + t2 = 0 + 13.5625 -1.0625t + t2 = 0 + 13.5625 Combine like terms: 0 + 13.5625 = 13.5625 -1.0625t + t2 = 13.5625 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 = 13.5625 + 0.2822265625 Reorder the terms: 0.2822265625 + -1.0625t + t2 = 13.5625 + 0.2822265625 Combine like terms: 13.5625 + 0.2822265625 = 13.8447265625 0.2822265625 + -1.0625t + t2 = 13.8447265625 Factor a perfect square on the left side: (t + -0.53125)(t + -0.53125) = 13.8447265625 Calculate the square root of the right side: 3.720850247 Break this problem into two subproblems by setting (t + -0.53125) equal to 3.720850247 and -3.720850247.Subproblem 1
t + -0.53125 = 3.720850247 Simplifying t + -0.53125 = 3.720850247 Reorder the terms: -0.53125 + t = 3.720850247 Solving -0.53125 + t = 3.720850247 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 = 3.720850247 + 0.53125 Combine like terms: -0.53125 + 0.53125 = 0.00000 0.00000 + t = 3.720850247 + 0.53125 t = 3.720850247 + 0.53125 Combine like terms: 3.720850247 + 0.53125 = 4.252100247 t = 4.252100247 Simplifying t = 4.252100247Subproblem 2
t + -0.53125 = -3.720850247 Simplifying t + -0.53125 = -3.720850247 Reorder the terms: -0.53125 + t = -3.720850247 Solving -0.53125 + t = -3.720850247 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 = -3.720850247 + 0.53125 Combine like terms: -0.53125 + 0.53125 = 0.00000 0.00000 + t = -3.720850247 + 0.53125 t = -3.720850247 + 0.53125 Combine like terms: -3.720850247 + 0.53125 = -3.189600247 t = -3.189600247 Simplifying t = -3.189600247Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.252100247, -3.189600247}
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