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Simplifying (0.9t2) + (8t) + -50 = 0 Reorder the terms: -50 + (8t) + (0.9t2) = 0 Solving -50 + (8t) + (0.9t2) = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 0.9 the coefficient of the squared term: Divide each side by '0.9'. -55.55555556 + (8.888888889t) + t2 = 0 Move the constant term to the right: Add '55.55555556' to each side of the equation. -55.55555556 + (8.888888889t) + 55.55555556 + t2 = 0 + 55.55555556 Reorder the terms: -55.55555556 + 55.55555556 + (8.888888889t) + t2 = 0 + 55.55555556 Combine like terms: -55.55555556 + 55.55555556 = 0.00000000 0.00000000 + (8.888888889t) + t2 = 0 + 55.55555556 (8.888888889t) + t2 = 0 + 55.55555556 Combine like terms: 0 + 55.55555556 = 55.55555556 (8.888888889t) + t2 = 55.55555556 The t term is (8.888888889t). Take half its coefficient (4.444444445). Square it (19.75308642) and add it to both sides. Add '19.75308642' to each side of the equation. (8.888888889t) + 19.75308642 + t2 = 55.55555556 + 19.75308642 Reorder the terms: 19.75308642 + (8.888888889t) + t2 = 55.55555556 + 19.75308642 Combine like terms: 55.55555556 + 19.75308642 = 75.30864198 19.75308642 + (8.888888889t) + t2 = 75.30864198 Factor a perfect square on the left side: ((t) + 4.444444445)((t) + 4.444444445) = 75.30864198 Calculate the square root of the right side: 8.678055196 Break this problem into two subproblems by setting ((t) + 4.444444445) equal to 8.678055196 and -8.678055196.Subproblem 1
(t) + 4.444444445 = 8.678055196 Simplifying (t) + 4.444444445 = 8.678055196 t + 4.444444445 = 8.678055196 Reorder the terms: 4.444444445 + t = 8.678055196 Solving 4.444444445 + t = 8.678055196 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-4.444444445' to each side of the equation. 4.444444445 + -4.444444445 + t = 8.678055196 + -4.444444445 Combine like terms: 4.444444445 + -4.444444445 = 0.000000000 0.000000000 + t = 8.678055196 + -4.444444445 t = 8.678055196 + -4.444444445 Combine like terms: 8.678055196 + -4.444444445 = 4.233610751 t = 4.233610751 Simplifying t = 4.233610751Subproblem 2
(t) + 4.444444445 = -8.678055196 Simplifying (t) + 4.444444445 = -8.678055196 t + 4.444444445 = -8.678055196 Reorder the terms: 4.444444445 + t = -8.678055196 Solving 4.444444445 + t = -8.678055196 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-4.444444445' to each side of the equation. 4.444444445 + -4.444444445 + t = -8.678055196 + -4.444444445 Combine like terms: 4.444444445 + -4.444444445 = 0.000000000 0.000000000 + t = -8.678055196 + -4.444444445 t = -8.678055196 + -4.444444445 Combine like terms: -8.678055196 + -4.444444445 = -13.122499641 t = -13.122499641 Simplifying t = -13.122499641Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.233610751, -13.122499641}
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