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Simplifying t2 + 5t + 6 = 666 Reorder the terms: 6 + 5t + t2 = 666 Solving 6 + 5t + t2 = 666 Solving for variable 't'. Reorder the terms: 6 + -666 + 5t + t2 = 666 + -666 Combine like terms: 6 + -666 = -660 -660 + 5t + t2 = 666 + -666 Combine like terms: 666 + -666 = 0 -660 + 5t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '660' to each side of the equation. -660 + 5t + 660 + t2 = 0 + 660 Reorder the terms: -660 + 660 + 5t + t2 = 0 + 660 Combine like terms: -660 + 660 = 0 0 + 5t + t2 = 0 + 660 5t + t2 = 0 + 660 Combine like terms: 0 + 660 = 660 5t + t2 = 660 The t term is 5t. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5t + 6.25 + t2 = 660 + 6.25 Reorder the terms: 6.25 + 5t + t2 = 660 + 6.25 Combine like terms: 660 + 6.25 = 666.25 6.25 + 5t + t2 = 666.25 Factor a perfect square on the left side: (t + 2.5)(t + 2.5) = 666.25 Calculate the square root of the right side: 25.811818998 Break this problem into two subproblems by setting (t + 2.5) equal to 25.811818998 and -25.811818998.Subproblem 1
t + 2.5 = 25.811818998 Simplifying t + 2.5 = 25.811818998 Reorder the terms: 2.5 + t = 25.811818998 Solving 2.5 + t = 25.811818998 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + t = 25.811818998 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + t = 25.811818998 + -2.5 t = 25.811818998 + -2.5 Combine like terms: 25.811818998 + -2.5 = 23.311818998 t = 23.311818998 Simplifying t = 23.311818998Subproblem 2
t + 2.5 = -25.811818998 Simplifying t + 2.5 = -25.811818998 Reorder the terms: 2.5 + t = -25.811818998 Solving 2.5 + t = -25.811818998 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + t = -25.811818998 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + t = -25.811818998 + -2.5 t = -25.811818998 + -2.5 Combine like terms: -25.811818998 + -2.5 = -28.311818998 t = -28.311818998 Simplifying t = -28.311818998Solution
The solution to the problem is based on the solutions from the subproblems. t = {23.311818998, -28.311818998}
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