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Simplifying 20t2 + t = 8 Reorder the terms: t + 20t2 = 8 Solving t + 20t2 = 8 Solving for variable 't'. Reorder the terms: -8 + t + 20t2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + t + 20t2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -0.4 + 0.05t + t2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + 0.05t + 0.4 + t2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + 0.05t + t2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + 0.05t + t2 = 0 + 0.4 0.05t + t2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 0.05t + t2 = 0.4 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 = 0.4 + 0.25 Reorder the terms: 0.25 + 0.05t + t2 = 0.4 + 0.25 Combine like terms: 0.4 + 0.25 = 0.65 0.25 + 0.05t + t2 = 0.65 Factor a perfect square on the left side: (t + 0.5)(t + 0.5) = 0.65 Calculate the square root of the right side: 0.806225775 Break this problem into two subproblems by setting (t + 0.5) equal to 0.806225775 and -0.806225775.Subproblem 1
t + 0.5 = 0.806225775 Simplifying t + 0.5 = 0.806225775 Reorder the terms: 0.5 + t = 0.806225775 Solving 0.5 + t = 0.806225775 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 = 0.806225775 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = 0.806225775 + -0.5 t = 0.806225775 + -0.5 Combine like terms: 0.806225775 + -0.5 = 0.306225775 t = 0.306225775 Simplifying t = 0.306225775Subproblem 2
t + 0.5 = -0.806225775 Simplifying t + 0.5 = -0.806225775 Reorder the terms: 0.5 + t = -0.806225775 Solving 0.5 + t = -0.806225775 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 = -0.806225775 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = -0.806225775 + -0.5 t = -0.806225775 + -0.5 Combine like terms: -0.806225775 + -0.5 = -1.306225775 t = -1.306225775 Simplifying t = -1.306225775Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.306225775, -1.306225775}
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