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Simplifying 4.9t2 + -11t + -97 = 0 Reorder the terms: -97 + -11t + 4.9t2 = 0 Solving -97 + -11t + 4.9t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -19.79591837 + -2.244897959t + t2 = 0 Move the constant term to the right: Add '19.79591837' to each side of the equation. -19.79591837 + -2.244897959t + 19.79591837 + t2 = 0 + 19.79591837 Reorder the terms: -19.79591837 + 19.79591837 + -2.244897959t + t2 = 0 + 19.79591837 Combine like terms: -19.79591837 + 19.79591837 = 0.00000000 0.00000000 + -2.244897959t + t2 = 0 + 19.79591837 -2.244897959t + t2 = 0 + 19.79591837 Combine like terms: 0 + 19.79591837 = 19.79591837 -2.244897959t + t2 = 19.79591837 The t term is -2.244897959t. Take half its coefficient (-1.12244898). Square it (1.259891713) and add it to both sides. Add '1.259891713' to each side of the equation. -2.244897959t + 1.259891713 + t2 = 19.79591837 + 1.259891713 Reorder the terms: 1.259891713 + -2.244897959t + t2 = 19.79591837 + 1.259891713 Combine like terms: 19.79591837 + 1.259891713 = 21.055810083 1.259891713 + -2.244897959t + t2 = 21.055810083 Factor a perfect square on the left side: (t + -1.12244898)(t + -1.12244898) = 21.055810083 Calculate the square root of the right side: 4.588661034 Break this problem into two subproblems by setting (t + -1.12244898) equal to 4.588661034 and -4.588661034.Subproblem 1
t + -1.12244898 = 4.588661034 Simplifying t + -1.12244898 = 4.588661034 Reorder the terms: -1.12244898 + t = 4.588661034 Solving -1.12244898 + t = 4.588661034 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.12244898' to each side of the equation. -1.12244898 + 1.12244898 + t = 4.588661034 + 1.12244898 Combine like terms: -1.12244898 + 1.12244898 = 0.00000000 0.00000000 + t = 4.588661034 + 1.12244898 t = 4.588661034 + 1.12244898 Combine like terms: 4.588661034 + 1.12244898 = 5.711110014 t = 5.711110014 Simplifying t = 5.711110014Subproblem 2
t + -1.12244898 = -4.588661034 Simplifying t + -1.12244898 = -4.588661034 Reorder the terms: -1.12244898 + t = -4.588661034 Solving -1.12244898 + t = -4.588661034 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.12244898' to each side of the equation. -1.12244898 + 1.12244898 + t = -4.588661034 + 1.12244898 Combine like terms: -1.12244898 + 1.12244898 = 0.00000000 0.00000000 + t = -4.588661034 + 1.12244898 t = -4.588661034 + 1.12244898 Combine like terms: -4.588661034 + 1.12244898 = -3.466212054 t = -3.466212054 Simplifying t = -3.466212054Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.711110014, -3.466212054}
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