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Simplifying t2 + 22t + 121 = 243 Reorder the terms: 121 + 22t + t2 = 243 Solving 121 + 22t + t2 = 243 Solving for variable 't'. Reorder the terms: 121 + -243 + 22t + t2 = 243 + -243 Combine like terms: 121 + -243 = -122 -122 + 22t + t2 = 243 + -243 Combine like terms: 243 + -243 = 0 -122 + 22t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '122' to each side of the equation. -122 + 22t + 122 + t2 = 0 + 122 Reorder the terms: -122 + 122 + 22t + t2 = 0 + 122 Combine like terms: -122 + 122 = 0 0 + 22t + t2 = 0 + 122 22t + t2 = 0 + 122 Combine like terms: 0 + 122 = 122 22t + t2 = 122 The t term is 22t. Take half its coefficient (11). Square it (121) and add it to both sides. Add '121' to each side of the equation. 22t + 121 + t2 = 122 + 121 Reorder the terms: 121 + 22t + t2 = 122 + 121 Combine like terms: 122 + 121 = 243 121 + 22t + t2 = 243 Factor a perfect square on the left side: (t + 11)(t + 11) = 243 Calculate the square root of the right side: 15.588457268 Break this problem into two subproblems by setting (t + 11) equal to 15.588457268 and -15.588457268.Subproblem 1
t + 11 = 15.588457268 Simplifying t + 11 = 15.588457268 Reorder the terms: 11 + t = 15.588457268 Solving 11 + t = 15.588457268 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + t = 15.588457268 + -11 Combine like terms: 11 + -11 = 0 0 + t = 15.588457268 + -11 t = 15.588457268 + -11 Combine like terms: 15.588457268 + -11 = 4.588457268 t = 4.588457268 Simplifying t = 4.588457268Subproblem 2
t + 11 = -15.588457268 Simplifying t + 11 = -15.588457268 Reorder the terms: 11 + t = -15.588457268 Solving 11 + t = -15.588457268 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + t = -15.588457268 + -11 Combine like terms: 11 + -11 = 0 0 + t = -15.588457268 + -11 t = -15.588457268 + -11 Combine like terms: -15.588457268 + -11 = -26.588457268 t = -26.588457268 Simplifying t = -26.588457268Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.588457268, -26.588457268}
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