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Simplifying 5t2 + 2t = 20 Reorder the terms: 2t + 5t2 = 20 Solving 2t + 5t2 = 20 Solving for variable 't'. Reorder the terms: -20 + 2t + 5t2 = 20 + -20 Combine like terms: 20 + -20 = 0 -20 + 2t + 5t2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -4 + 0.4t + t2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 0.4t + 4 + t2 = 0 + 4 Reorder the terms: -4 + 4 + 0.4t + t2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 0.4t + t2 = 0 + 4 0.4t + t2 = 0 + 4 Combine like terms: 0 + 4 = 4 0.4t + t2 = 4 The t term is 0.4t. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4t + 0.04 + t2 = 4 + 0.04 Reorder the terms: 0.04 + 0.4t + t2 = 4 + 0.04 Combine like terms: 4 + 0.04 = 4.04 0.04 + 0.4t + t2 = 4.04 Factor a perfect square on the left side: (t + 0.2)(t + 0.2) = 4.04 Calculate the square root of the right side: 2.009975124 Break this problem into two subproblems by setting (t + 0.2) equal to 2.009975124 and -2.009975124.Subproblem 1
t + 0.2 = 2.009975124 Simplifying t + 0.2 = 2.009975124 Reorder the terms: 0.2 + t = 2.009975124 Solving 0.2 + t = 2.009975124 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + t = 2.009975124 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + t = 2.009975124 + -0.2 t = 2.009975124 + -0.2 Combine like terms: 2.009975124 + -0.2 = 1.809975124 t = 1.809975124 Simplifying t = 1.809975124Subproblem 2
t + 0.2 = -2.009975124 Simplifying t + 0.2 = -2.009975124 Reorder the terms: 0.2 + t = -2.009975124 Solving 0.2 + t = -2.009975124 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + t = -2.009975124 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + t = -2.009975124 + -0.2 t = -2.009975124 + -0.2 Combine like terms: -2.009975124 + -0.2 = -2.209975124 t = -2.209975124 Simplifying t = -2.209975124Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.809975124, -2.209975124}
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