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Simplifying 16t2 + -17t + 4 = 8 Reorder the terms: 4 + -17t + 16t2 = 8 Solving 4 + -17t + 16t2 = 8 Solving for variable 't'. Reorder the terms: 4 + -8 + -17t + 16t2 = 8 + -8 Combine like terms: 4 + -8 = -4 -4 + -17t + 16t2 = 8 + -8 Combine like terms: 8 + -8 = 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 = 0.5322265625 0.2822265625 + -1.0625t + t2 = 0.5322265625 Factor a perfect square on the left side: (t + -0.53125)(t + -0.53125) = 0.5322265625 Calculate the square root of the right side: 0.729538596 Break this problem into two subproblems by setting (t + -0.53125) equal to 0.729538596 and -0.729538596.Subproblem 1
t + -0.53125 = 0.729538596 Simplifying t + -0.53125 = 0.729538596 Reorder the terms: -0.53125 + t = 0.729538596 Solving -0.53125 + t = 0.729538596 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 = 0.729538596 + 0.53125 Combine like terms: -0.53125 + 0.53125 = 0.00000 0.00000 + t = 0.729538596 + 0.53125 t = 0.729538596 + 0.53125 Combine like terms: 0.729538596 + 0.53125 = 1.260788596 t = 1.260788596 Simplifying t = 1.260788596Subproblem 2
t + -0.53125 = -0.729538596 Simplifying t + -0.53125 = -0.729538596 Reorder the terms: -0.53125 + t = -0.729538596 Solving -0.53125 + t = -0.729538596 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 = -0.729538596 + 0.53125 Combine like terms: -0.53125 + 0.53125 = 0.00000 0.00000 + t = -0.729538596 + 0.53125 t = -0.729538596 + 0.53125 Combine like terms: -0.729538596 + 0.53125 = -0.198288596 t = -0.198288596 Simplifying t = -0.198288596Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.260788596, -0.198288596}
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