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Simplifying 20 = 5t2 + 30t + 1 Reorder the terms: 20 = 1 + 30t + 5t2 Solving 20 = 1 + 30t + 5t2 Solving for variable 't'. Combine like terms: 20 + -1 = 19 19 + -30t + -5t2 = 1 + 30t + 5t2 + -1 + -30t + -5t2 Reorder the terms: 19 + -30t + -5t2 = 1 + -1 + 30t + -30t + 5t2 + -5t2 Combine like terms: 1 + -1 = 0 19 + -30t + -5t2 = 0 + 30t + -30t + 5t2 + -5t2 19 + -30t + -5t2 = 30t + -30t + 5t2 + -5t2 Combine like terms: 30t + -30t = 0 19 + -30t + -5t2 = 0 + 5t2 + -5t2 19 + -30t + -5t2 = 5t2 + -5t2 Combine like terms: 5t2 + -5t2 = 0 19 + -30t + -5t2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -3.8 + 6t + t2 = 0 Move the constant term to the right: Add '3.8' to each side of the equation. -3.8 + 6t + 3.8 + t2 = 0 + 3.8 Reorder the terms: -3.8 + 3.8 + 6t + t2 = 0 + 3.8 Combine like terms: -3.8 + 3.8 = 0.0 0.0 + 6t + t2 = 0 + 3.8 6t + t2 = 0 + 3.8 Combine like terms: 0 + 3.8 = 3.8 6t + t2 = 3.8 The t term is 6t. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6t + 9 + t2 = 3.8 + 9 Reorder the terms: 9 + 6t + t2 = 3.8 + 9 Combine like terms: 3.8 + 9 = 12.8 9 + 6t + t2 = 12.8 Factor a perfect square on the left side: (t + 3)(t + 3) = 12.8 Calculate the square root of the right side: 3.577708764 Break this problem into two subproblems by setting (t + 3) equal to 3.577708764 and -3.577708764.Subproblem 1
t + 3 = 3.577708764 Simplifying t + 3 = 3.577708764 Reorder the terms: 3 + t = 3.577708764 Solving 3 + t = 3.577708764 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + t = 3.577708764 + -3 Combine like terms: 3 + -3 = 0 0 + t = 3.577708764 + -3 t = 3.577708764 + -3 Combine like terms: 3.577708764 + -3 = 0.577708764 t = 0.577708764 Simplifying t = 0.577708764Subproblem 2
t + 3 = -3.577708764 Simplifying t + 3 = -3.577708764 Reorder the terms: 3 + t = -3.577708764 Solving 3 + t = -3.577708764 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + t = -3.577708764 + -3 Combine like terms: 3 + -3 = 0 0 + t = -3.577708764 + -3 t = -3.577708764 + -3 Combine like terms: -3.577708764 + -3 = -6.577708764 t = -6.577708764 Simplifying t = -6.577708764Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.577708764, -6.577708764}
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