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Simplifying t2 + 22t + 121 = 246 Reorder the terms: 121 + 22t + t2 = 246 Solving 121 + 22t + t2 = 246 Solving for variable 't'. Reorder the terms: 121 + -246 + 22t + t2 = 246 + -246 Combine like terms: 121 + -246 = -125 -125 + 22t + t2 = 246 + -246 Combine like terms: 246 + -246 = 0 -125 + 22t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '125' to each side of the equation. -125 + 22t + 125 + t2 = 0 + 125 Reorder the terms: -125 + 125 + 22t + t2 = 0 + 125 Combine like terms: -125 + 125 = 0 0 + 22t + t2 = 0 + 125 22t + t2 = 0 + 125 Combine like terms: 0 + 125 = 125 22t + t2 = 125 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 = 125 + 121 Reorder the terms: 121 + 22t + t2 = 125 + 121 Combine like terms: 125 + 121 = 246 121 + 22t + t2 = 246 Factor a perfect square on the left side: (t + 11)(t + 11) = 246 Calculate the square root of the right side: 15.684387141 Break this problem into two subproblems by setting (t + 11) equal to 15.684387141 and -15.684387141.Subproblem 1
t + 11 = 15.684387141 Simplifying t + 11 = 15.684387141 Reorder the terms: 11 + t = 15.684387141 Solving 11 + t = 15.684387141 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 = 15.684387141 + -11 Combine like terms: 11 + -11 = 0 0 + t = 15.684387141 + -11 t = 15.684387141 + -11 Combine like terms: 15.684387141 + -11 = 4.684387141 t = 4.684387141 Simplifying t = 4.684387141Subproblem 2
t + 11 = -15.684387141 Simplifying t + 11 = -15.684387141 Reorder the terms: 11 + t = -15.684387141 Solving 11 + t = -15.684387141 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 = -15.684387141 + -11 Combine like terms: 11 + -11 = 0 0 + t = -15.684387141 + -11 t = -15.684387141 + -11 Combine like terms: -15.684387141 + -11 = -26.684387141 t = -26.684387141 Simplifying t = -26.684387141Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.684387141, -26.684387141}
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