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Simplifying -245 = 63.1906t + 0.5 * -9.8t2 Multiply 0.5 * -9.8 -245 = 63.1906t + -4.9t2 Solving -245 = 63.1906t + -4.9t2 Solving for variable 't'. Reorder the terms: -245 + -63.1906t + 4.9t2 = 63.1906t + -63.1906t + -4.9t2 + 4.9t2 Combine like terms: 63.1906t + -63.1906t = 0.0000 -245 + -63.1906t + 4.9t2 = 0.0000 + -4.9t2 + 4.9t2 -245 + -63.1906t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -245 + -63.1906t + 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'. -50 + -12.89604082t + t2 = 0 Move the constant term to the right: Add '50' to each side of the equation. -50 + -12.89604082t + 50 + t2 = 0 + 50 Reorder the terms: -50 + 50 + -12.89604082t + t2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + -12.89604082t + t2 = 0 + 50 -12.89604082t + t2 = 0 + 50 Combine like terms: 0 + 50 = 50 -12.89604082t + t2 = 50 The t term is -12.89604082t. Take half its coefficient (-6.44802041). Square it (41.57696721) and add it to both sides. Add '41.57696721' to each side of the equation. -12.89604082t + 41.57696721 + t2 = 50 + 41.57696721 Reorder the terms: 41.57696721 + -12.89604082t + t2 = 50 + 41.57696721 Combine like terms: 50 + 41.57696721 = 91.57696721 41.57696721 + -12.89604082t + t2 = 91.57696721 Factor a perfect square on the left side: (t + -6.44802041)(t + -6.44802041) = 91.57696721 Calculate the square root of the right side: 9.56958553 Break this problem into two subproblems by setting (t + -6.44802041) equal to 9.56958553 and -9.56958553.Subproblem 1
t + -6.44802041 = 9.56958553 Simplifying t + -6.44802041 = 9.56958553 Reorder the terms: -6.44802041 + t = 9.56958553 Solving -6.44802041 + t = 9.56958553 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.44802041' to each side of the equation. -6.44802041 + 6.44802041 + t = 9.56958553 + 6.44802041 Combine like terms: -6.44802041 + 6.44802041 = 0.00000000 0.00000000 + t = 9.56958553 + 6.44802041 t = 9.56958553 + 6.44802041 Combine like terms: 9.56958553 + 6.44802041 = 16.01760594 t = 16.01760594 Simplifying t = 16.01760594Subproblem 2
t + -6.44802041 = -9.56958553 Simplifying t + -6.44802041 = -9.56958553 Reorder the terms: -6.44802041 + t = -9.56958553 Solving -6.44802041 + t = -9.56958553 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.44802041' to each side of the equation. -6.44802041 + 6.44802041 + t = -9.56958553 + 6.44802041 Combine like terms: -6.44802041 + 6.44802041 = 0.00000000 0.00000000 + t = -9.56958553 + 6.44802041 t = -9.56958553 + 6.44802041 Combine like terms: -9.56958553 + 6.44802041 = -3.12156512 t = -3.12156512 Simplifying t = -3.12156512Solution
The solution to the problem is based on the solutions from the subproblems. t = {16.01760594, -3.12156512}
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