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Simplifying t2 + -20t + -19 = 0 Reorder the terms: -19 + -20t + t2 = 0 Solving -19 + -20t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '19' to each side of the equation. -19 + -20t + 19 + t2 = 0 + 19 Reorder the terms: -19 + 19 + -20t + t2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + -20t + t2 = 0 + 19 -20t + t2 = 0 + 19 Combine like terms: 0 + 19 = 19 -20t + t2 = 19 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 = 19 + 100 Reorder the terms: 100 + -20t + t2 = 19 + 100 Combine like terms: 19 + 100 = 119 100 + -20t + t2 = 119 Factor a perfect square on the left side: (t + -10)(t + -10) = 119 Calculate the square root of the right side: 10.908712115 Break this problem into two subproblems by setting (t + -10) equal to 10.908712115 and -10.908712115.Subproblem 1
t + -10 = 10.908712115 Simplifying t + -10 = 10.908712115 Reorder the terms: -10 + t = 10.908712115 Solving -10 + t = 10.908712115 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 = 10.908712115 + 10 Combine like terms: -10 + 10 = 0 0 + t = 10.908712115 + 10 t = 10.908712115 + 10 Combine like terms: 10.908712115 + 10 = 20.908712115 t = 20.908712115 Simplifying t = 20.908712115Subproblem 2
t + -10 = -10.908712115 Simplifying t + -10 = -10.908712115 Reorder the terms: -10 + t = -10.908712115 Solving -10 + t = -10.908712115 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 = -10.908712115 + 10 Combine like terms: -10 + 10 = 0 0 + t = -10.908712115 + 10 t = -10.908712115 + 10 Combine like terms: -10.908712115 + 10 = -0.908712115 t = -0.908712115 Simplifying t = -0.908712115Solution
The solution to the problem is based on the solutions from the subproblems. t = {20.908712115, -0.908712115}
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