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Simplifying t2 + -13t + 2 = 0 Reorder the terms: 2 + -13t + t2 = 0 Solving 2 + -13t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + -13t + -2 + t2 = 0 + -2 Reorder the terms: 2 + -2 + -13t + t2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -13t + t2 = 0 + -2 -13t + t2 = 0 + -2 Combine like terms: 0 + -2 = -2 -13t + t2 = -2 The t term is -13t. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13t + 42.25 + t2 = -2 + 42.25 Reorder the terms: 42.25 + -13t + t2 = -2 + 42.25 Combine like terms: -2 + 42.25 = 40.25 42.25 + -13t + t2 = 40.25 Factor a perfect square on the left side: (t + -6.5)(t + -6.5) = 40.25 Calculate the square root of the right side: 6.34428877 Break this problem into two subproblems by setting (t + -6.5) equal to 6.34428877 and -6.34428877.Subproblem 1
t + -6.5 = 6.34428877 Simplifying t + -6.5 = 6.34428877 Reorder the terms: -6.5 + t = 6.34428877 Solving -6.5 + t = 6.34428877 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + t = 6.34428877 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + t = 6.34428877 + 6.5 t = 6.34428877 + 6.5 Combine like terms: 6.34428877 + 6.5 = 12.84428877 t = 12.84428877 Simplifying t = 12.84428877Subproblem 2
t + -6.5 = -6.34428877 Simplifying t + -6.5 = -6.34428877 Reorder the terms: -6.5 + t = -6.34428877 Solving -6.5 + t = -6.34428877 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + t = -6.34428877 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + t = -6.34428877 + 6.5 t = -6.34428877 + 6.5 Combine like terms: -6.34428877 + 6.5 = 0.15571123 t = 0.15571123 Simplifying t = 0.15571123Solution
The solution to the problem is based on the solutions from the subproblems. t = {12.84428877, 0.15571123}
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