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Simplifying -0.025t2 + -0.5t + 50 = 0 Reorder the terms: 50 + -0.5t + -0.025t2 = 0 Solving 50 + -0.5t + -0.025t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -0.025 the coefficient of the squared term: Divide each side by '-0.025'. -2000 + 20t + t2 = 0 Move the constant term to the right: Add '2000' to each side of the equation. -2000 + 20t + 2000 + t2 = 0 + 2000 Reorder the terms: -2000 + 2000 + 20t + t2 = 0 + 2000 Combine like terms: -2000 + 2000 = 0 0 + 20t + t2 = 0 + 2000 20t + t2 = 0 + 2000 Combine like terms: 0 + 2000 = 2000 20t + t2 = 2000 The t term is 20t. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20t + 100 + t2 = 2000 + 100 Reorder the terms: 100 + 20t + t2 = 2000 + 100 Combine like terms: 2000 + 100 = 2100 100 + 20t + t2 = 2100 Factor a perfect square on the left side: (t + 10)(t + 10) = 2100 Calculate the square root of the right side: 45.82575695 Break this problem into two subproblems by setting (t + 10) equal to 45.82575695 and -45.82575695.Subproblem 1
t + 10 = 45.82575695 Simplifying t + 10 = 45.82575695 Reorder the terms: 10 + t = 45.82575695 Solving 10 + t = 45.82575695 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + t = 45.82575695 + -10 Combine like terms: 10 + -10 = 0 0 + t = 45.82575695 + -10 t = 45.82575695 + -10 Combine like terms: 45.82575695 + -10 = 35.82575695 t = 35.82575695 Simplifying t = 35.82575695Subproblem 2
t + 10 = -45.82575695 Simplifying t + 10 = -45.82575695 Reorder the terms: 10 + t = -45.82575695 Solving 10 + t = -45.82575695 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + t = -45.82575695 + -10 Combine like terms: 10 + -10 = 0 0 + t = -45.82575695 + -10 t = -45.82575695 + -10 Combine like terms: -45.82575695 + -10 = -55.82575695 t = -55.82575695 Simplifying t = -55.82575695Solution
The solution to the problem is based on the solutions from the subproblems. t = {35.82575695, -55.82575695}
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