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Simplifying 16t2 + -288t = 32 Reorder the terms: -288t + 16t2 = 32 Solving -288t + 16t2 = 32 Solving for variable 't'. Reorder the terms: -32 + -288t + 16t2 = 32 + -32 Combine like terms: 32 + -32 = 0 -32 + -288t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(-2 + -18t + t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-2 + -18t + t2)' equal to zero and attempt to solve: Simplifying -2 + -18t + t2 = 0 Solving -2 + -18t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + -18t + 2 + t2 = 0 + 2 Reorder the terms: -2 + 2 + -18t + t2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -18t + t2 = 0 + 2 -18t + t2 = 0 + 2 Combine like terms: 0 + 2 = 2 -18t + t2 = 2 The t term is -18t. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18t + 81 + t2 = 2 + 81 Reorder the terms: 81 + -18t + t2 = 2 + 81 Combine like terms: 2 + 81 = 83 81 + -18t + t2 = 83 Factor a perfect square on the left side: (t + -9)(t + -9) = 83 Calculate the square root of the right side: 9.110433579 Break this problem into two subproblems by setting (t + -9) equal to 9.110433579 and -9.110433579.Subproblem 1
t + -9 = 9.110433579 Simplifying t + -9 = 9.110433579 Reorder the terms: -9 + t = 9.110433579 Solving -9 + t = 9.110433579 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + t = 9.110433579 + 9 Combine like terms: -9 + 9 = 0 0 + t = 9.110433579 + 9 t = 9.110433579 + 9 Combine like terms: 9.110433579 + 9 = 18.110433579 t = 18.110433579 Simplifying t = 18.110433579Subproblem 2
t + -9 = -9.110433579 Simplifying t + -9 = -9.110433579 Reorder the terms: -9 + t = -9.110433579 Solving -9 + t = -9.110433579 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + t = -9.110433579 + 9 Combine like terms: -9 + 9 = 0 0 + t = -9.110433579 + 9 t = -9.110433579 + 9 Combine like terms: -9.110433579 + 9 = -0.110433579 t = -0.110433579 Simplifying t = -0.110433579Solution
The solution to the problem is based on the solutions from the subproblems. t = {18.110433579, -0.110433579}Solution
t = {18.110433579, -0.110433579}
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