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Simplifying 11 + 5t + -4.9t2 = 0 Solving 11 + 5t + -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'. -2.244897959 + -1.020408163t + t2 = 0 Move the constant term to the right: Add '2.244897959' to each side of the equation. -2.244897959 + -1.020408163t + 2.244897959 + t2 = 0 + 2.244897959 Reorder the terms: -2.244897959 + 2.244897959 + -1.020408163t + t2 = 0 + 2.244897959 Combine like terms: -2.244897959 + 2.244897959 = 0.000000000 0.000000000 + -1.020408163t + t2 = 0 + 2.244897959 -1.020408163t + t2 = 0 + 2.244897959 Combine like terms: 0 + 2.244897959 = 2.244897959 -1.020408163t + t2 = 2.244897959 The t term is -1.020408163t. Take half its coefficient (-0.5102040815). Square it (0.2603082048) and add it to both sides. Add '0.2603082048' to each side of the equation. -1.020408163t + 0.2603082048 + t2 = 2.244897959 + 0.2603082048 Reorder the terms: 0.2603082048 + -1.020408163t + t2 = 2.244897959 + 0.2603082048 Combine like terms: 2.244897959 + 0.2603082048 = 2.5052061638 0.2603082048 + -1.020408163t + t2 = 2.5052061638 Factor a perfect square on the left side: (t + -0.5102040815)(t + -0.5102040815) = 2.5052061638 Calculate the square root of the right side: 1.582784307 Break this problem into two subproblems by setting (t + -0.5102040815) equal to 1.582784307 and -1.582784307.Subproblem 1
t + -0.5102040815 = 1.582784307 Simplifying t + -0.5102040815 = 1.582784307 Reorder the terms: -0.5102040815 + t = 1.582784307 Solving -0.5102040815 + t = 1.582784307 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5102040815' to each side of the equation. -0.5102040815 + 0.5102040815 + t = 1.582784307 + 0.5102040815 Combine like terms: -0.5102040815 + 0.5102040815 = 0.0000000000 0.0000000000 + t = 1.582784307 + 0.5102040815 t = 1.582784307 + 0.5102040815 Combine like terms: 1.582784307 + 0.5102040815 = 2.0929883885 t = 2.0929883885 Simplifying t = 2.0929883885Subproblem 2
t + -0.5102040815 = -1.582784307 Simplifying t + -0.5102040815 = -1.582784307 Reorder the terms: -0.5102040815 + t = -1.582784307 Solving -0.5102040815 + t = -1.582784307 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5102040815' to each side of the equation. -0.5102040815 + 0.5102040815 + t = -1.582784307 + 0.5102040815 Combine like terms: -0.5102040815 + 0.5102040815 = 0.0000000000 0.0000000000 + t = -1.582784307 + 0.5102040815 t = -1.582784307 + 0.5102040815 Combine like terms: -1.582784307 + 0.5102040815 = -1.0725802255 t = -1.0725802255 Simplifying t = -1.0725802255Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.0929883885, -1.0725802255}
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