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Simplifying 500 + 11t + -4.9t2 = 0 Solving 500 + 11t + -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'. -102.0408163 + -2.244897959t + t2 = 0 Move the constant term to the right: Add '102.0408163' to each side of the equation. -102.0408163 + -2.244897959t + 102.0408163 + t2 = 0 + 102.0408163 Reorder the terms: -102.0408163 + 102.0408163 + -2.244897959t + t2 = 0 + 102.0408163 Combine like terms: -102.0408163 + 102.0408163 = 0.0000000 0.0000000 + -2.244897959t + t2 = 0 + 102.0408163 -2.244897959t + t2 = 0 + 102.0408163 Combine like terms: 0 + 102.0408163 = 102.0408163 -2.244897959t + t2 = 102.0408163 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 = 102.0408163 + 1.259891713 Reorder the terms: 1.259891713 + -2.244897959t + t2 = 102.0408163 + 1.259891713 Combine like terms: 102.0408163 + 1.259891713 = 103.300708013 1.259891713 + -2.244897959t + t2 = 103.300708013 Factor a perfect square on the left side: (t + -1.12244898)(t + -1.12244898) = 103.300708013 Calculate the square root of the right side: 10.163695588 Break this problem into two subproblems by setting (t + -1.12244898) equal to 10.163695588 and -10.163695588.Subproblem 1
t + -1.12244898 = 10.163695588 Simplifying t + -1.12244898 = 10.163695588 Reorder the terms: -1.12244898 + t = 10.163695588 Solving -1.12244898 + t = 10.163695588 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 = 10.163695588 + 1.12244898 Combine like terms: -1.12244898 + 1.12244898 = 0.00000000 0.00000000 + t = 10.163695588 + 1.12244898 t = 10.163695588 + 1.12244898 Combine like terms: 10.163695588 + 1.12244898 = 11.286144568 t = 11.286144568 Simplifying t = 11.286144568Subproblem 2
t + -1.12244898 = -10.163695588 Simplifying t + -1.12244898 = -10.163695588 Reorder the terms: -1.12244898 + t = -10.163695588 Solving -1.12244898 + t = -10.163695588 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 = -10.163695588 + 1.12244898 Combine like terms: -1.12244898 + 1.12244898 = 0.00000000 0.00000000 + t = -10.163695588 + 1.12244898 t = -10.163695588 + 1.12244898 Combine like terms: -10.163695588 + 1.12244898 = -9.041246608 t = -9.041246608 Simplifying t = -9.041246608Solution
The solution to the problem is based on the solutions from the subproblems. t = {11.286144568, -9.041246608}
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