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Simplifying 0.2 = 20t + 5t2 Solving 0.2 = 20t + 5t2 Solving for variable 't'. Reorder the terms: 0.2 + -20t + -5t2 = 20t + -20t + 5t2 + -5t2 Combine like terms: 20t + -20t = 0 0.2 + -20t + -5t2 = 0 + 5t2 + -5t2 0.2 + -20t + -5t2 = 5t2 + -5t2 Combine like terms: 5t2 + -5t2 = 0 0.2 + -20t + -5t2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -0.04 + 4t + t2 = 0 Move the constant term to the right: Add '0.04' to each side of the equation. -0.04 + 4t + 0.04 + t2 = 0 + 0.04 Reorder the terms: -0.04 + 0.04 + 4t + t2 = 0 + 0.04 Combine like terms: -0.04 + 0.04 = 0.00 0.00 + 4t + t2 = 0 + 0.04 4t + t2 = 0 + 0.04 Combine like terms: 0 + 0.04 = 0.04 4t + t2 = 0.04 The t term is 4t. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4t + 4 + t2 = 0.04 + 4 Reorder the terms: 4 + 4t + t2 = 0.04 + 4 Combine like terms: 0.04 + 4 = 4.04 4 + 4t + t2 = 4.04 Factor a perfect square on the left side: (t + 2)(t + 2) = 4.04 Calculate the square root of the right side: 2.009975124 Break this problem into two subproblems by setting (t + 2) equal to 2.009975124 and -2.009975124.Subproblem 1
t + 2 = 2.009975124 Simplifying t + 2 = 2.009975124 Reorder the terms: 2 + t = 2.009975124 Solving 2 + t = 2.009975124 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + t = 2.009975124 + -2 Combine like terms: 2 + -2 = 0 0 + t = 2.009975124 + -2 t = 2.009975124 + -2 Combine like terms: 2.009975124 + -2 = 0.009975124 t = 0.009975124 Simplifying t = 0.009975124Subproblem 2
t + 2 = -2.009975124 Simplifying t + 2 = -2.009975124 Reorder the terms: 2 + t = -2.009975124 Solving 2 + t = -2.009975124 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + t = -2.009975124 + -2 Combine like terms: 2 + -2 = 0 0 + t = -2.009975124 + -2 t = -2.009975124 + -2 Combine like terms: -2.009975124 + -2 = -4.009975124 t = -4.009975124 Simplifying t = -4.009975124Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.009975124, -4.009975124}
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