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Simplifying 0 = -4.9t2 + 11t + 0.3 Reorder the terms: 0 = 0.3 + 11t + -4.9t2 Solving 0 = 0.3 + 11t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -0.3 = -0.3 -0.3 + -11t + 4.9t2 = 0.3 + 11t + -4.9t2 + -0.3 + -11t + 4.9t2 Reorder the terms: -0.3 + -11t + 4.9t2 = 0.3 + -0.3 + 11t + -11t + -4.9t2 + 4.9t2 Combine like terms: 0.3 + -0.3 = 0.0 -0.3 + -11t + 4.9t2 = 0.0 + 11t + -11t + -4.9t2 + 4.9t2 -0.3 + -11t + 4.9t2 = 11t + -11t + -4.9t2 + 4.9t2 Combine like terms: 11t + -11t = 0 -0.3 + -11t + 4.9t2 = 0 + -4.9t2 + 4.9t2 -0.3 + -11t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -0.3 + -11t + 4.9t2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -0.0612244898 + -2.244897959t + t2 = 0 Move the constant term to the right: Add '0.0612244898' to each side of the equation. -0.0612244898 + -2.244897959t + 0.0612244898 + t2 = 0 + 0.0612244898 Reorder the terms: -0.0612244898 + 0.0612244898 + -2.244897959t + t2 = 0 + 0.0612244898 Combine like terms: -0.0612244898 + 0.0612244898 = 0.0000000000 0.0000000000 + -2.244897959t + t2 = 0 + 0.0612244898 -2.244897959t + t2 = 0 + 0.0612244898 Combine like terms: 0 + 0.0612244898 = 0.0612244898 -2.244897959t + t2 = 0.0612244898 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 = 0.0612244898 + 1.259891713 Reorder the terms: 1.259891713 + -2.244897959t + t2 = 0.0612244898 + 1.259891713 Combine like terms: 0.0612244898 + 1.259891713 = 1.3211162028 1.259891713 + -2.244897959t + t2 = 1.3211162028 Factor a perfect square on the left side: (t + -1.12244898)(t + -1.12244898) = 1.3211162028 Calculate the square root of the right side: 1.149398192 Break this problem into two subproblems by setting (t + -1.12244898) equal to 1.149398192 and -1.149398192.Subproblem 1
t + -1.12244898 = 1.149398192 Simplifying t + -1.12244898 = 1.149398192 Reorder the terms: -1.12244898 + t = 1.149398192 Solving -1.12244898 + t = 1.149398192 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 = 1.149398192 + 1.12244898 Combine like terms: -1.12244898 + 1.12244898 = 0.00000000 0.00000000 + t = 1.149398192 + 1.12244898 t = 1.149398192 + 1.12244898 Combine like terms: 1.149398192 + 1.12244898 = 2.271847172 t = 2.271847172 Simplifying t = 2.271847172Subproblem 2
t + -1.12244898 = -1.149398192 Simplifying t + -1.12244898 = -1.149398192 Reorder the terms: -1.12244898 + t = -1.149398192 Solving -1.12244898 + t = -1.149398192 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 = -1.149398192 + 1.12244898 Combine like terms: -1.12244898 + 1.12244898 = 0.00000000 0.00000000 + t = -1.149398192 + 1.12244898 t = -1.149398192 + 1.12244898 Combine like terms: -1.149398192 + 1.12244898 = -0.026949212 t = -0.026949212 Simplifying t = -0.026949212Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.271847172, -0.026949212}
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