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Simplifying t2 + 20t + 100 = 25 + 100 Reorder the terms: 100 + 20t + t2 = 25 + 100 Combine like terms: 25 + 100 = 125 100 + 20t + t2 = 125 Solving 100 + 20t + t2 = 125 Solving for variable 't'. Reorder the terms: 100 + -125 + 20t + t2 = 125 + -125 Combine like terms: 100 + -125 = -25 -25 + 20t + t2 = 125 + -125 Combine like terms: 125 + -125 = 0 -25 + 20t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + 20t + 25 + t2 = 0 + 25 Reorder the terms: -25 + 25 + 20t + t2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 20t + t2 = 0 + 25 20t + t2 = 0 + 25 Combine like terms: 0 + 25 = 25 20t + t2 = 25 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 = 25 + 100 Reorder the terms: 100 + 20t + t2 = 25 + 100 Combine like terms: 25 + 100 = 125 100 + 20t + t2 = 125 Factor a perfect square on the left side: (t + 10)(t + 10) = 125 Calculate the square root of the right side: 11.180339887 Break this problem into two subproblems by setting (t + 10) equal to 11.180339887 and -11.180339887.Subproblem 1
t + 10 = 11.180339887 Simplifying t + 10 = 11.180339887 Reorder the terms: 10 + t = 11.180339887 Solving 10 + t = 11.180339887 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 = 11.180339887 + -10 Combine like terms: 10 + -10 = 0 0 + t = 11.180339887 + -10 t = 11.180339887 + -10 Combine like terms: 11.180339887 + -10 = 1.180339887 t = 1.180339887 Simplifying t = 1.180339887Subproblem 2
t + 10 = -11.180339887 Simplifying t + 10 = -11.180339887 Reorder the terms: 10 + t = -11.180339887 Solving 10 + t = -11.180339887 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 = -11.180339887 + -10 Combine like terms: 10 + -10 = 0 0 + t = -11.180339887 + -10 t = -11.180339887 + -10 Combine like terms: -11.180339887 + -10 = -21.180339887 t = -21.180339887 Simplifying t = -21.180339887Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.180339887, -21.180339887}
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