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Simplifying 2.85t2 + 50t = 1 Reorder the terms: 50t + 2.85t2 = 1 Solving 50t + 2.85t2 = 1 Solving for variable 't'. Reorder the terms: -1 + 50t + 2.85t2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + 50t + 2.85t2 = 0 Begin completing the square. Divide all terms by 2.85 the coefficient of the squared term: Divide each side by '2.85'. -0.350877193 + 17.54385965t + t2 = 0 Move the constant term to the right: Add '0.350877193' to each side of the equation. -0.350877193 + 17.54385965t + 0.350877193 + t2 = 0 + 0.350877193 Reorder the terms: -0.350877193 + 0.350877193 + 17.54385965t + t2 = 0 + 0.350877193 Combine like terms: -0.350877193 + 0.350877193 = 0.000000000 0.000000000 + 17.54385965t + t2 = 0 + 0.350877193 17.54385965t + t2 = 0 + 0.350877193 Combine like terms: 0 + 0.350877193 = 0.350877193 17.54385965t + t2 = 0.350877193 The t term is 17.54385965t. Take half its coefficient (8.771929825). Square it (76.94675285) and add it to both sides. Add '76.94675285' to each side of the equation. 17.54385965t + 76.94675285 + t2 = 0.350877193 + 76.94675285 Reorder the terms: 76.94675285 + 17.54385965t + t2 = 0.350877193 + 76.94675285 Combine like terms: 0.350877193 + 76.94675285 = 77.297630043 76.94675285 + 17.54385965t + t2 = 77.297630043 Factor a perfect square on the left side: (t + 8.771929825)(t + 8.771929825) = 77.297630043 Calculate the square root of the right side: 8.791907077 Break this problem into two subproblems by setting (t + 8.771929825) equal to 8.791907077 and -8.791907077.Subproblem 1
t + 8.771929825 = 8.791907077 Simplifying t + 8.771929825 = 8.791907077 Reorder the terms: 8.771929825 + t = 8.791907077 Solving 8.771929825 + t = 8.791907077 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-8.771929825' to each side of the equation. 8.771929825 + -8.771929825 + t = 8.791907077 + -8.771929825 Combine like terms: 8.771929825 + -8.771929825 = 0.000000000 0.000000000 + t = 8.791907077 + -8.771929825 t = 8.791907077 + -8.771929825 Combine like terms: 8.791907077 + -8.771929825 = 0.019977252 t = 0.019977252 Simplifying t = 0.019977252Subproblem 2
t + 8.771929825 = -8.791907077 Simplifying t + 8.771929825 = -8.791907077 Reorder the terms: 8.771929825 + t = -8.791907077 Solving 8.771929825 + t = -8.791907077 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-8.771929825' to each side of the equation. 8.771929825 + -8.771929825 + t = -8.791907077 + -8.771929825 Combine like terms: 8.771929825 + -8.771929825 = 0.000000000 0.000000000 + t = -8.791907077 + -8.771929825 t = -8.791907077 + -8.771929825 Combine like terms: -8.791907077 + -8.771929825 = -17.563836902 t = -17.563836902 Simplifying t = -17.563836902Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.019977252, -17.563836902}
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