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Simplifying 0.2t2 + 20t + -500 = 0 Reorder the terms: -500 + 20t + 0.2t2 = 0 Solving -500 + 20t + 0.2t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 0.2 the coefficient of the squared term: Divide each side by '0.2'. -2500 + 100t + t2 = 0 Move the constant term to the right: Add '2500' to each side of the equation. -2500 + 100t + 2500 + t2 = 0 + 2500 Reorder the terms: -2500 + 2500 + 100t + t2 = 0 + 2500 Combine like terms: -2500 + 2500 = 0 0 + 100t + t2 = 0 + 2500 100t + t2 = 0 + 2500 Combine like terms: 0 + 2500 = 2500 100t + t2 = 2500 The t term is 100t. Take half its coefficient (50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. 100t + 2500 + t2 = 2500 + 2500 Reorder the terms: 2500 + 100t + t2 = 2500 + 2500 Combine like terms: 2500 + 2500 = 5000 2500 + 100t + t2 = 5000 Factor a perfect square on the left side: (t + 50)(t + 50) = 5000 Calculate the square root of the right side: 70.710678119 Break this problem into two subproblems by setting (t + 50) equal to 70.710678119 and -70.710678119.Subproblem 1
t + 50 = 70.710678119 Simplifying t + 50 = 70.710678119 Reorder the terms: 50 + t = 70.710678119 Solving 50 + t = 70.710678119 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + t = 70.710678119 + -50 Combine like terms: 50 + -50 = 0 0 + t = 70.710678119 + -50 t = 70.710678119 + -50 Combine like terms: 70.710678119 + -50 = 20.710678119 t = 20.710678119 Simplifying t = 20.710678119Subproblem 2
t + 50 = -70.710678119 Simplifying t + 50 = -70.710678119 Reorder the terms: 50 + t = -70.710678119 Solving 50 + t = -70.710678119 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + t = -70.710678119 + -50 Combine like terms: 50 + -50 = 0 0 + t = -70.710678119 + -50 t = -70.710678119 + -50 Combine like terms: -70.710678119 + -50 = -120.710678119 t = -120.710678119 Simplifying t = -120.710678119Solution
The solution to the problem is based on the solutions from the subproblems. t = {20.710678119, -120.710678119}
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