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Simplifying t2 + -1t + -40 = 0 Reorder the terms: -40 + -1t + t2 = 0 Solving -40 + -1t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '40' to each side of the equation. -40 + -1t + 40 + t2 = 0 + 40 Reorder the terms: -40 + 40 + -1t + t2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + -1t + t2 = 0 + 40 -1t + t2 = 0 + 40 Combine like terms: 0 + 40 = 40 -1t + t2 = 40 The t term is -1t. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1t + 0.25 + t2 = 40 + 0.25 Reorder the terms: 0.25 + -1t + t2 = 40 + 0.25 Combine like terms: 40 + 0.25 = 40.25 0.25 + -1t + t2 = 40.25 Factor a perfect square on the left side: (t + -0.5)(t + -0.5) = 40.25 Calculate the square root of the right side: 6.34428877 Break this problem into two subproblems by setting (t + -0.5) equal to 6.34428877 and -6.34428877.Subproblem 1
t + -0.5 = 6.34428877 Simplifying t + -0.5 = 6.34428877 Reorder the terms: -0.5 + t = 6.34428877 Solving -0.5 + t = 6.34428877 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + t = 6.34428877 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = 6.34428877 + 0.5 t = 6.34428877 + 0.5 Combine like terms: 6.34428877 + 0.5 = 6.84428877 t = 6.84428877 Simplifying t = 6.84428877Subproblem 2
t + -0.5 = -6.34428877 Simplifying t + -0.5 = -6.34428877 Reorder the terms: -0.5 + t = -6.34428877 Solving -0.5 + t = -6.34428877 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + t = -6.34428877 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = -6.34428877 + 0.5 t = -6.34428877 + 0.5 Combine like terms: -6.34428877 + 0.5 = -5.84428877 t = -5.84428877 Simplifying t = -5.84428877Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.84428877, -5.84428877}
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