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Simplifying 4.9t2 + 11t = 76 Reorder the terms: 11t + 4.9t2 = 76 Solving 11t + 4.9t2 = 76 Solving for variable 't'. Reorder the terms: -76 + 11t + 4.9t2 = 76 + -76 Combine like terms: 76 + -76 = 0 -76 + 11t + 4.9t2 = 0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -15.51020408 + 2.244897959t + t2 = 0 Move the constant term to the right: Add '15.51020408' to each side of the equation. -15.51020408 + 2.244897959t + 15.51020408 + t2 = 0 + 15.51020408 Reorder the terms: -15.51020408 + 15.51020408 + 2.244897959t + t2 = 0 + 15.51020408 Combine like terms: -15.51020408 + 15.51020408 = 0.00000000 0.00000000 + 2.244897959t + t2 = 0 + 15.51020408 2.244897959t + t2 = 0 + 15.51020408 Combine like terms: 0 + 15.51020408 = 15.51020408 2.244897959t + t2 = 15.51020408 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 = 15.51020408 + 1.259891713 Reorder the terms: 1.259891713 + 2.244897959t + t2 = 15.51020408 + 1.259891713 Combine like terms: 15.51020408 + 1.259891713 = 16.770095793 1.259891713 + 2.244897959t + t2 = 16.770095793 Factor a perfect square on the left side: (t + 1.12244898)(t + 1.12244898) = 16.770095793 Calculate the square root of the right side: 4.095130742 Break this problem into two subproblems by setting (t + 1.12244898) equal to 4.095130742 and -4.095130742.Subproblem 1
t + 1.12244898 = 4.095130742 Simplifying t + 1.12244898 = 4.095130742 Reorder the terms: 1.12244898 + t = 4.095130742 Solving 1.12244898 + t = 4.095130742 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 = 4.095130742 + -1.12244898 Combine like terms: 1.12244898 + -1.12244898 = 0.00000000 0.00000000 + t = 4.095130742 + -1.12244898 t = 4.095130742 + -1.12244898 Combine like terms: 4.095130742 + -1.12244898 = 2.972681762 t = 2.972681762 Simplifying t = 2.972681762Subproblem 2
t + 1.12244898 = -4.095130742 Simplifying t + 1.12244898 = -4.095130742 Reorder the terms: 1.12244898 + t = -4.095130742 Solving 1.12244898 + t = -4.095130742 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 = -4.095130742 + -1.12244898 Combine like terms: 1.12244898 + -1.12244898 = 0.00000000 0.00000000 + t = -4.095130742 + -1.12244898 t = -4.095130742 + -1.12244898 Combine like terms: -4.095130742 + -1.12244898 = -5.217579722 t = -5.217579722 Simplifying t = -5.217579722Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.972681762, -5.217579722}
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