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Simplifying t2 + -11t + -10 = 0 Reorder the terms: -10 + -11t + t2 = 0 Solving -10 + -11t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + -11t + 10 + t2 = 0 + 10 Reorder the terms: -10 + 10 + -11t + t2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -11t + t2 = 0 + 10 -11t + t2 = 0 + 10 Combine like terms: 0 + 10 = 10 -11t + t2 = 10 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 = 10 + 30.25 Reorder the terms: 30.25 + -11t + t2 = 10 + 30.25 Combine like terms: 10 + 30.25 = 40.25 30.25 + -11t + t2 = 40.25 Factor a perfect square on the left side: (t + -5.5)(t + -5.5) = 40.25 Calculate the square root of the right side: 6.34428877 Break this problem into two subproblems by setting (t + -5.5) equal to 6.34428877 and -6.34428877.Subproblem 1
t + -5.5 = 6.34428877 Simplifying t + -5.5 = 6.34428877 Reorder the terms: -5.5 + t = 6.34428877 Solving -5.5 + t = 6.34428877 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 = 6.34428877 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + t = 6.34428877 + 5.5 t = 6.34428877 + 5.5 Combine like terms: 6.34428877 + 5.5 = 11.84428877 t = 11.84428877 Simplifying t = 11.84428877Subproblem 2
t + -5.5 = -6.34428877 Simplifying t + -5.5 = -6.34428877 Reorder the terms: -5.5 + t = -6.34428877 Solving -5.5 + t = -6.34428877 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 = -6.34428877 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + t = -6.34428877 + 5.5 t = -6.34428877 + 5.5 Combine like terms: -6.34428877 + 5.5 = -0.84428877 t = -0.84428877 Simplifying t = -0.84428877Solution
The solution to the problem is based on the solutions from the subproblems. t = {11.84428877, -0.84428877}
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