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Simplifying t2 + -24t + 32 = 0 Reorder the terms: 32 + -24t + t2 = 0 Solving 32 + -24t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '-32' to each side of the equation. 32 + -24t + -32 + t2 = 0 + -32 Reorder the terms: 32 + -32 + -24t + t2 = 0 + -32 Combine like terms: 32 + -32 = 0 0 + -24t + t2 = 0 + -32 -24t + t2 = 0 + -32 Combine like terms: 0 + -32 = -32 -24t + t2 = -32 The t term is -24t. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24t + 144 + t2 = -32 + 144 Reorder the terms: 144 + -24t + t2 = -32 + 144 Combine like terms: -32 + 144 = 112 144 + -24t + t2 = 112 Factor a perfect square on the left side: (t + -12)(t + -12) = 112 Calculate the square root of the right side: 10.583005244 Break this problem into two subproblems by setting (t + -12) equal to 10.583005244 and -10.583005244.Subproblem 1
t + -12 = 10.583005244 Simplifying t + -12 = 10.583005244 Reorder the terms: -12 + t = 10.583005244 Solving -12 + t = 10.583005244 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + t = 10.583005244 + 12 Combine like terms: -12 + 12 = 0 0 + t = 10.583005244 + 12 t = 10.583005244 + 12 Combine like terms: 10.583005244 + 12 = 22.583005244 t = 22.583005244 Simplifying t = 22.583005244Subproblem 2
t + -12 = -10.583005244 Simplifying t + -12 = -10.583005244 Reorder the terms: -12 + t = -10.583005244 Solving -12 + t = -10.583005244 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + t = -10.583005244 + 12 Combine like terms: -12 + 12 = 0 0 + t = -10.583005244 + 12 t = -10.583005244 + 12 Combine like terms: -10.583005244 + 12 = 1.416994756 t = 1.416994756 Simplifying t = 1.416994756Solution
The solution to the problem is based on the solutions from the subproblems. t = {22.583005244, 1.416994756}
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