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Simplifying t2 + -20t + -20 = 0 Reorder the terms: -20 + -20t + t2 = 0 Solving -20 + -20t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + -20t + 20 + t2 = 0 + 20 Reorder the terms: -20 + 20 + -20t + t2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -20t + t2 = 0 + 20 -20t + t2 = 0 + 20 Combine like terms: 0 + 20 = 20 -20t + t2 = 20 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 = 20 + 100 Reorder the terms: 100 + -20t + t2 = 20 + 100 Combine like terms: 20 + 100 = 120 100 + -20t + t2 = 120 Factor a perfect square on the left side: (t + -10)(t + -10) = 120 Calculate the square root of the right side: 10.95445115 Break this problem into two subproblems by setting (t + -10) equal to 10.95445115 and -10.95445115.Subproblem 1
t + -10 = 10.95445115 Simplifying t + -10 = 10.95445115 Reorder the terms: -10 + t = 10.95445115 Solving -10 + t = 10.95445115 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 = 10.95445115 + 10 Combine like terms: -10 + 10 = 0 0 + t = 10.95445115 + 10 t = 10.95445115 + 10 Combine like terms: 10.95445115 + 10 = 20.95445115 t = 20.95445115 Simplifying t = 20.95445115Subproblem 2
t + -10 = -10.95445115 Simplifying t + -10 = -10.95445115 Reorder the terms: -10 + t = -10.95445115 Solving -10 + t = -10.95445115 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 = -10.95445115 + 10 Combine like terms: -10 + 10 = 0 0 + t = -10.95445115 + 10 t = -10.95445115 + 10 Combine like terms: -10.95445115 + 10 = -0.95445115 t = -0.95445115 Simplifying t = -0.95445115Solution
The solution to the problem is based on the solutions from the subproblems. t = {20.95445115, -0.95445115}
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