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Simplifying 16t2 + -64t + -23 = 0 Reorder the terms: -23 + -64t + 16t2 = 0 Solving -23 + -64t + 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'. -1.4375 + -4t + t2 = 0 Move the constant term to the right: Add '1.4375' to each side of the equation. -1.4375 + -4t + 1.4375 + t2 = 0 + 1.4375 Reorder the terms: -1.4375 + 1.4375 + -4t + t2 = 0 + 1.4375 Combine like terms: -1.4375 + 1.4375 = 0.0000 0.0000 + -4t + t2 = 0 + 1.4375 -4t + t2 = 0 + 1.4375 Combine like terms: 0 + 1.4375 = 1.4375 -4t + t2 = 1.4375 The t term is -4t. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4t + 4 + t2 = 1.4375 + 4 Reorder the terms: 4 + -4t + t2 = 1.4375 + 4 Combine like terms: 1.4375 + 4 = 5.4375 4 + -4t + t2 = 5.4375 Factor a perfect square on the left side: (t + -2)(t + -2) = 5.4375 Calculate the square root of the right side: 2.331844763 Break this problem into two subproblems by setting (t + -2) equal to 2.331844763 and -2.331844763.Subproblem 1
t + -2 = 2.331844763 Simplifying t + -2 = 2.331844763 Reorder the terms: -2 + t = 2.331844763 Solving -2 + t = 2.331844763 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = 2.331844763 + 2 Combine like terms: -2 + 2 = 0 0 + t = 2.331844763 + 2 t = 2.331844763 + 2 Combine like terms: 2.331844763 + 2 = 4.331844763 t = 4.331844763 Simplifying t = 4.331844763Subproblem 2
t + -2 = -2.331844763 Simplifying t + -2 = -2.331844763 Reorder the terms: -2 + t = -2.331844763 Solving -2 + t = -2.331844763 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = -2.331844763 + 2 Combine like terms: -2 + 2 = 0 0 + t = -2.331844763 + 2 t = -2.331844763 + 2 Combine like terms: -2.331844763 + 2 = -0.331844763 t = -0.331844763 Simplifying t = -0.331844763Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.331844763, -0.331844763}
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