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Simplifying t2 + -11t + 15 = 0 Reorder the terms: 15 + -11t + t2 = 0 Solving 15 + -11t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '-15' to each side of the equation. 15 + -11t + -15 + t2 = 0 + -15 Reorder the terms: 15 + -15 + -11t + t2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -11t + t2 = 0 + -15 -11t + t2 = 0 + -15 Combine like terms: 0 + -15 = -15 -11t + t2 = -15 The t term is -11t. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11t + 30.25 + t2 = -15 + 30.25 Reorder the terms: 30.25 + -11t + t2 = -15 + 30.25 Combine like terms: -15 + 30.25 = 15.25 30.25 + -11t + t2 = 15.25 Factor a perfect square on the left side: (t + -5.5)(t + -5.5) = 15.25 Calculate the square root of the right side: 3.905124838 Break this problem into two subproblems by setting (t + -5.5) equal to 3.905124838 and -3.905124838.Subproblem 1
t + -5.5 = 3.905124838 Simplifying t + -5.5 = 3.905124838 Reorder the terms: -5.5 + t = 3.905124838 Solving -5.5 + t = 3.905124838 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + t = 3.905124838 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + t = 3.905124838 + 5.5 t = 3.905124838 + 5.5 Combine like terms: 3.905124838 + 5.5 = 9.405124838 t = 9.405124838 Simplifying t = 9.405124838Subproblem 2
t + -5.5 = -3.905124838 Simplifying t + -5.5 = -3.905124838 Reorder the terms: -5.5 + t = -3.905124838 Solving -5.5 + t = -3.905124838 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + t = -3.905124838 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + t = -3.905124838 + 5.5 t = -3.905124838 + 5.5 Combine like terms: -3.905124838 + 5.5 = 1.594875162 t = 1.594875162 Simplifying t = 1.594875162Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.405124838, 1.594875162}
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