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Simplifying 20t2 + t + 1 = 0 Reorder the terms: 1 + t + 20t2 = 0 Solving 1 + t + 20t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. 0.05 + 0.05t + t2 = 0 Move the constant term to the right: Add '-0.05' to each side of the equation. 0.05 + 0.05t + -0.05 + t2 = 0 + -0.05 Reorder the terms: 0.05 + -0.05 + 0.05t + t2 = 0 + -0.05 Combine like terms: 0.05 + -0.05 = 0.00 0.00 + 0.05t + t2 = 0 + -0.05 0.05t + t2 = 0 + -0.05 Combine like terms: 0 + -0.05 = -0.05 0.05t + t2 = -0.05 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. 0.05t + 0.25 + t2 = -0.05 + 0.25 Reorder the terms: 0.25 + 0.05t + t2 = -0.05 + 0.25 Combine like terms: -0.05 + 0.25 = 0.2 0.25 + 0.05t + t2 = 0.2 Factor a perfect square on the left side: (t + 0.5)(t + 0.5) = 0.2 Calculate the square root of the right side: 0.447213596 Break this problem into two subproblems by setting (t + 0.5) equal to 0.447213596 and -0.447213596.Subproblem 1
t + 0.5 = 0.447213596 Simplifying t + 0.5 = 0.447213596 Reorder the terms: 0.5 + t = 0.447213596 Solving 0.5 + t = 0.447213596 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 = 0.447213596 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = 0.447213596 + -0.5 t = 0.447213596 + -0.5 Combine like terms: 0.447213596 + -0.5 = -0.052786404 t = -0.052786404 Simplifying t = -0.052786404Subproblem 2
t + 0.5 = -0.447213596 Simplifying t + 0.5 = -0.447213596 Reorder the terms: 0.5 + t = -0.447213596 Solving 0.5 + t = -0.447213596 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 = -0.447213596 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = -0.447213596 + -0.5 t = -0.447213596 + -0.5 Combine like terms: -0.447213596 + -0.5 = -0.947213596 t = -0.947213596 Simplifying t = -0.947213596Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.052786404, -0.947213596}
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