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Simplifying 0.5t2 + 20t + -100 = 0 Reorder the terms: -100 + 20t + 0.5t2 = 0 Solving -100 + 20t + 0.5t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -200 + 40t + t2 = 0 Move the constant term to the right: Add '200' to each side of the equation. -200 + 40t + 200 + t2 = 0 + 200 Reorder the terms: -200 + 200 + 40t + t2 = 0 + 200 Combine like terms: -200 + 200 = 0 0 + 40t + t2 = 0 + 200 40t + t2 = 0 + 200 Combine like terms: 0 + 200 = 200 40t + t2 = 200 The t term is 40t. Take half its coefficient (20). Square it (400) and add it to both sides. Add '400' to each side of the equation. 40t + 400 + t2 = 200 + 400 Reorder the terms: 400 + 40t + t2 = 200 + 400 Combine like terms: 200 + 400 = 600 400 + 40t + t2 = 600 Factor a perfect square on the left side: (t + 20)(t + 20) = 600 Calculate the square root of the right side: 24.494897428 Break this problem into two subproblems by setting (t + 20) equal to 24.494897428 and -24.494897428.Subproblem 1
t + 20 = 24.494897428 Simplifying t + 20 = 24.494897428 Reorder the terms: 20 + t = 24.494897428 Solving 20 + t = 24.494897428 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + t = 24.494897428 + -20 Combine like terms: 20 + -20 = 0 0 + t = 24.494897428 + -20 t = 24.494897428 + -20 Combine like terms: 24.494897428 + -20 = 4.494897428 t = 4.494897428 Simplifying t = 4.494897428Subproblem 2
t + 20 = -24.494897428 Simplifying t + 20 = -24.494897428 Reorder the terms: 20 + t = -24.494897428 Solving 20 + t = -24.494897428 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + t = -24.494897428 + -20 Combine like terms: 20 + -20 = 0 0 + t = -24.494897428 + -20 t = -24.494897428 + -20 Combine like terms: -24.494897428 + -20 = -44.494897428 t = -44.494897428 Simplifying t = -44.494897428Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.494897428, -44.494897428}
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