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Simplifying -2t2 + -32t = 50 Reorder the terms: -32t + -2t2 = 50 Solving -32t + -2t2 = 50 Solving for variable 't'. Reorder the terms: -50 + -32t + -2t2 = 50 + -50 Combine like terms: 50 + -50 = 0 -50 + -32t + -2t2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(25 + 16t + t2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(25 + 16t + t2)' equal to zero and attempt to solve: Simplifying 25 + 16t + t2 = 0 Solving 25 + 16t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-25' to each side of the equation. 25 + 16t + -25 + t2 = 0 + -25 Reorder the terms: 25 + -25 + 16t + t2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + 16t + t2 = 0 + -25 16t + t2 = 0 + -25 Combine like terms: 0 + -25 = -25 16t + t2 = -25 The t term is 16t. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16t + 64 + t2 = -25 + 64 Reorder the terms: 64 + 16t + t2 = -25 + 64 Combine like terms: -25 + 64 = 39 64 + 16t + t2 = 39 Factor a perfect square on the left side: (t + 8)(t + 8) = 39 Calculate the square root of the right side: 6.244997998 Break this problem into two subproblems by setting (t + 8) equal to 6.244997998 and -6.244997998.Subproblem 1
t + 8 = 6.244997998 Simplifying t + 8 = 6.244997998 Reorder the terms: 8 + t = 6.244997998 Solving 8 + t = 6.244997998 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + t = 6.244997998 + -8 Combine like terms: 8 + -8 = 0 0 + t = 6.244997998 + -8 t = 6.244997998 + -8 Combine like terms: 6.244997998 + -8 = -1.755002002 t = -1.755002002 Simplifying t = -1.755002002Subproblem 2
t + 8 = -6.244997998 Simplifying t + 8 = -6.244997998 Reorder the terms: 8 + t = -6.244997998 Solving 8 + t = -6.244997998 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + t = -6.244997998 + -8 Combine like terms: 8 + -8 = 0 0 + t = -6.244997998 + -8 t = -6.244997998 + -8 Combine like terms: -6.244997998 + -8 = -14.244997998 t = -14.244997998 Simplifying t = -14.244997998Solution
The solution to the problem is based on the solutions from the subproblems. t = {-1.755002002, -14.244997998}Solution
t = {-1.755002002, -14.244997998}
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