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Simplifying t2 + t + -44 = 0 Reorder the terms: -44 + t + t2 = 0 Solving -44 + t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '44' to each side of the equation. -44 + t + 44 + t2 = 0 + 44 Reorder the terms: -44 + 44 + t + t2 = 0 + 44 Combine like terms: -44 + 44 = 0 0 + t + t2 = 0 + 44 t + t2 = 0 + 44 Combine like terms: 0 + 44 = 44 t + t2 = 44 The t term is t. 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. t + 0.25 + t2 = 44 + 0.25 Reorder the terms: 0.25 + t + t2 = 44 + 0.25 Combine like terms: 44 + 0.25 = 44.25 0.25 + t + t2 = 44.25 Factor a perfect square on the left side: (t + 0.5)(t + 0.5) = 44.25 Calculate the square root of the right side: 6.652067348 Break this problem into two subproblems by setting (t + 0.5) equal to 6.652067348 and -6.652067348.Subproblem 1
t + 0.5 = 6.652067348 Simplifying t + 0.5 = 6.652067348 Reorder the terms: 0.5 + t = 6.652067348 Solving 0.5 + t = 6.652067348 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 = 6.652067348 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = 6.652067348 + -0.5 t = 6.652067348 + -0.5 Combine like terms: 6.652067348 + -0.5 = 6.152067348 t = 6.152067348 Simplifying t = 6.152067348Subproblem 2
t + 0.5 = -6.652067348 Simplifying t + 0.5 = -6.652067348 Reorder the terms: 0.5 + t = -6.652067348 Solving 0.5 + t = -6.652067348 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 = -6.652067348 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = -6.652067348 + -0.5 t = -6.652067348 + -0.5 Combine like terms: -6.652067348 + -0.5 = -7.152067348 t = -7.152067348 Simplifying t = -7.152067348Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.152067348, -7.152067348}
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