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Simplifying 0.0795t2 + -0.904t + 1.877 = 0 Reorder the terms: 1.877 + -0.904t + 0.0795t2 = 0 Solving 1.877 + -0.904t + 0.0795t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 0.0795 the coefficient of the squared term: Divide each side by '0.0795'. 23.61006289 + -11.37106918t + t2 = 0 Move the constant term to the right: Add '-23.61006289' to each side of the equation. 23.61006289 + -11.37106918t + -23.61006289 + t2 = 0 + -23.61006289 Reorder the terms: 23.61006289 + -23.61006289 + -11.37106918t + t2 = 0 + -23.61006289 Combine like terms: 23.61006289 + -23.61006289 = 0.00000000 0.00000000 + -11.37106918t + t2 = 0 + -23.61006289 -11.37106918t + t2 = 0 + -23.61006289 Combine like terms: 0 + -23.61006289 = -23.61006289 -11.37106918t + t2 = -23.61006289 The t term is -11.37106918t. Take half its coefficient (-5.68553459). Square it (32.32530357) and add it to both sides. Add '32.32530357' to each side of the equation. -11.37106918t + 32.32530357 + t2 = -23.61006289 + 32.32530357 Reorder the terms: 32.32530357 + -11.37106918t + t2 = -23.61006289 + 32.32530357 Combine like terms: -23.61006289 + 32.32530357 = 8.71524068 32.32530357 + -11.37106918t + t2 = 8.71524068 Factor a perfect square on the left side: (t + -5.68553459)(t + -5.68553459) = 8.71524068 Calculate the square root of the right side: 2.952158647 Break this problem into two subproblems by setting (t + -5.68553459) equal to 2.952158647 and -2.952158647.Subproblem 1
t + -5.68553459 = 2.952158647 Simplifying t + -5.68553459 = 2.952158647 Reorder the terms: -5.68553459 + t = 2.952158647 Solving -5.68553459 + t = 2.952158647 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.68553459' to each side of the equation. -5.68553459 + 5.68553459 + t = 2.952158647 + 5.68553459 Combine like terms: -5.68553459 + 5.68553459 = 0.00000000 0.00000000 + t = 2.952158647 + 5.68553459 t = 2.952158647 + 5.68553459 Combine like terms: 2.952158647 + 5.68553459 = 8.637693237 t = 8.637693237 Simplifying t = 8.637693237Subproblem 2
t + -5.68553459 = -2.952158647 Simplifying t + -5.68553459 = -2.952158647 Reorder the terms: -5.68553459 + t = -2.952158647 Solving -5.68553459 + t = -2.952158647 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.68553459' to each side of the equation. -5.68553459 + 5.68553459 + t = -2.952158647 + 5.68553459 Combine like terms: -5.68553459 + 5.68553459 = 0.00000000 0.00000000 + t = -2.952158647 + 5.68553459 t = -2.952158647 + 5.68553459 Combine like terms: -2.952158647 + 5.68553459 = 2.733375943 t = 2.733375943 Simplifying t = 2.733375943Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.637693237, 2.733375943}
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