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Simplifying 5t2 + 20t + 4 = 0 Reorder the terms: 4 + 20t + 5t2 = 0 Solving 4 + 20t + 5t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.8 + 4t + t2 = 0 Move the constant term to the right: Add '-0.8' to each side of the equation. 0.8 + 4t + -0.8 + t2 = 0 + -0.8 Reorder the terms: 0.8 + -0.8 + 4t + t2 = 0 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + 4t + t2 = 0 + -0.8 4t + t2 = 0 + -0.8 Combine like terms: 0 + -0.8 = -0.8 4t + t2 = -0.8 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 = -0.8 + 4 Reorder the terms: 4 + 4t + t2 = -0.8 + 4 Combine like terms: -0.8 + 4 = 3.2 4 + 4t + t2 = 3.2 Factor a perfect square on the left side: (t + 2)(t + 2) = 3.2 Calculate the square root of the right side: 1.788854382 Break this problem into two subproblems by setting (t + 2) equal to 1.788854382 and -1.788854382.Subproblem 1
t + 2 = 1.788854382 Simplifying t + 2 = 1.788854382 Reorder the terms: 2 + t = 1.788854382 Solving 2 + t = 1.788854382 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 = 1.788854382 + -2 Combine like terms: 2 + -2 = 0 0 + t = 1.788854382 + -2 t = 1.788854382 + -2 Combine like terms: 1.788854382 + -2 = -0.211145618 t = -0.211145618 Simplifying t = -0.211145618Subproblem 2
t + 2 = -1.788854382 Simplifying t + 2 = -1.788854382 Reorder the terms: 2 + t = -1.788854382 Solving 2 + t = -1.788854382 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 = -1.788854382 + -2 Combine like terms: 2 + -2 = 0 0 + t = -1.788854382 + -2 t = -1.788854382 + -2 Combine like terms: -1.788854382 + -2 = -3.788854382 t = -3.788854382 Simplifying t = -3.788854382Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.211145618, -3.788854382}
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