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Simplifying t2 + -3.673t + 2.245 = 0 Reorder the terms: 2.245 + -3.673t + t2 = 0 Solving 2.245 + -3.673t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '-2.245' to each side of the equation. 2.245 + -3.673t + -2.245 + t2 = 0 + -2.245 Reorder the terms: 2.245 + -2.245 + -3.673t + t2 = 0 + -2.245 Combine like terms: 2.245 + -2.245 = 0.000 0.000 + -3.673t + t2 = 0 + -2.245 -3.673t + t2 = 0 + -2.245 Combine like terms: 0 + -2.245 = -2.245 -3.673t + t2 = -2.245 The t term is -3.673t. Take half its coefficient (-1.8365). Square it (3.37273225) and add it to both sides. Add '3.37273225' to each side of the equation. -3.673t + 3.37273225 + t2 = -2.245 + 3.37273225 Reorder the terms: 3.37273225 + -3.673t + t2 = -2.245 + 3.37273225 Combine like terms: -2.245 + 3.37273225 = 1.12773225 3.37273225 + -3.673t + t2 = 1.12773225 Factor a perfect square on the left side: (t + -1.8365)(t + -1.8365) = 1.12773225 Calculate the square root of the right side: 1.061947386 Break this problem into two subproblems by setting (t + -1.8365) equal to 1.061947386 and -1.061947386.Subproblem 1
t + -1.8365 = 1.061947386 Simplifying t + -1.8365 = 1.061947386 Reorder the terms: -1.8365 + t = 1.061947386 Solving -1.8365 + t = 1.061947386 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.8365' to each side of the equation. -1.8365 + 1.8365 + t = 1.061947386 + 1.8365 Combine like terms: -1.8365 + 1.8365 = 0.0000 0.0000 + t = 1.061947386 + 1.8365 t = 1.061947386 + 1.8365 Combine like terms: 1.061947386 + 1.8365 = 2.898447386 t = 2.898447386 Simplifying t = 2.898447386Subproblem 2
t + -1.8365 = -1.061947386 Simplifying t + -1.8365 = -1.061947386 Reorder the terms: -1.8365 + t = -1.061947386 Solving -1.8365 + t = -1.061947386 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.8365' to each side of the equation. -1.8365 + 1.8365 + t = -1.061947386 + 1.8365 Combine like terms: -1.8365 + 1.8365 = 0.0000 0.0000 + t = -1.061947386 + 1.8365 t = -1.061947386 + 1.8365 Combine like terms: -1.061947386 + 1.8365 = 0.774552614 t = 0.774552614 Simplifying t = 0.774552614Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.898447386, 0.774552614}
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