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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 = 3.189600247 t = 3.189600247 Simplifying t = 3.189600247Subproblem 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 = -4.252100247 t = -4.252100247 Simplifying t = -4.252100247Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.189600247, -4.252100247}
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