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Simplifying 5t2 + 2t + -50 = 0 Reorder the terms: -50 + 2t + 5t2 = 0 Solving -50 + 2t + 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'. -10 + 0.4t + t2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + 0.4t + 10 + t2 = 0 + 10 Reorder the terms: -10 + 10 + 0.4t + t2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 0.4t + t2 = 0 + 10 0.4t + t2 = 0 + 10 Combine like terms: 0 + 10 = 10 0.4t + t2 = 10 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 = 10 + 0.04 Reorder the terms: 0.04 + 0.4t + t2 = 10 + 0.04 Combine like terms: 10 + 0.04 = 10.04 0.04 + 0.4t + t2 = 10.04 Factor a perfect square on the left side: (t + 0.2)(t + 0.2) = 10.04 Calculate the square root of the right side: 3.168595904 Break this problem into two subproblems by setting (t + 0.2) equal to 3.168595904 and -3.168595904.Subproblem 1
t + 0.2 = 3.168595904 Simplifying t + 0.2 = 3.168595904 Reorder the terms: 0.2 + t = 3.168595904 Solving 0.2 + t = 3.168595904 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 = 3.168595904 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + t = 3.168595904 + -0.2 t = 3.168595904 + -0.2 Combine like terms: 3.168595904 + -0.2 = 2.968595904 t = 2.968595904 Simplifying t = 2.968595904Subproblem 2
t + 0.2 = -3.168595904 Simplifying t + 0.2 = -3.168595904 Reorder the terms: 0.2 + t = -3.168595904 Solving 0.2 + t = -3.168595904 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 = -3.168595904 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + t = -3.168595904 + -0.2 t = -3.168595904 + -0.2 Combine like terms: -3.168595904 + -0.2 = -3.368595904 t = -3.368595904 Simplifying t = -3.368595904Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.968595904, -3.368595904}
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