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Simplifying 16t * t + 25t + -52 = 0 Multiply t * t 16t2 + 25t + -52 = 0 Reorder the terms: -52 + 25t + 16t2 = 0 Solving -52 + 25t + 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'. -3.25 + 1.5625t + t2 = 0 Move the constant term to the right: Add '3.25' to each side of the equation. -3.25 + 1.5625t + 3.25 + t2 = 0 + 3.25 Reorder the terms: -3.25 + 3.25 + 1.5625t + t2 = 0 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + 1.5625t + t2 = 0 + 3.25 1.5625t + t2 = 0 + 3.25 Combine like terms: 0 + 3.25 = 3.25 1.5625t + t2 = 3.25 The t term is 1.5625t. Take half its coefficient (0.78125). Square it (0.6103515625) and add it to both sides. Add '0.6103515625' to each side of the equation. 1.5625t + 0.6103515625 + t2 = 3.25 + 0.6103515625 Reorder the terms: 0.6103515625 + 1.5625t + t2 = 3.25 + 0.6103515625 Combine like terms: 3.25 + 0.6103515625 = 3.8603515625 0.6103515625 + 1.5625t + t2 = 3.8603515625 Factor a perfect square on the left side: (t + 0.78125)(t + 0.78125) = 3.8603515625 Calculate the square root of the right side: 1.964777739 Break this problem into two subproblems by setting (t + 0.78125) equal to 1.964777739 and -1.964777739.Subproblem 1
t + 0.78125 = 1.964777739 Simplifying t + 0.78125 = 1.964777739 Reorder the terms: 0.78125 + t = 1.964777739 Solving 0.78125 + t = 1.964777739 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.78125' to each side of the equation. 0.78125 + -0.78125 + t = 1.964777739 + -0.78125 Combine like terms: 0.78125 + -0.78125 = 0.00000 0.00000 + t = 1.964777739 + -0.78125 t = 1.964777739 + -0.78125 Combine like terms: 1.964777739 + -0.78125 = 1.183527739 t = 1.183527739 Simplifying t = 1.183527739Subproblem 2
t + 0.78125 = -1.964777739 Simplifying t + 0.78125 = -1.964777739 Reorder the terms: 0.78125 + t = -1.964777739 Solving 0.78125 + t = -1.964777739 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.78125' to each side of the equation. 0.78125 + -0.78125 + t = -1.964777739 + -0.78125 Combine like terms: 0.78125 + -0.78125 = 0.00000 0.00000 + t = -1.964777739 + -0.78125 t = -1.964777739 + -0.78125 Combine like terms: -1.964777739 + -0.78125 = -2.746027739 t = -2.746027739 Simplifying t = -2.746027739Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.183527739, -2.746027739}
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