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Simplifying -16t2 + 1074.667t + -5000 = 0 Reorder the terms: -5000 + 1074.667t + -16t2 = 0 Solving -5000 + 1074.667t + -16t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. 312.5 + -67.1666875t + t2 = 0 Move the constant term to the right: Add '-312.5' to each side of the equation. 312.5 + -67.1666875t + -312.5 + t2 = 0 + -312.5 Reorder the terms: 312.5 + -312.5 + -67.1666875t + t2 = 0 + -312.5 Combine like terms: 312.5 + -312.5 = 0.0 0.0 + -67.1666875t + t2 = 0 + -312.5 -67.1666875t + t2 = 0 + -312.5 Combine like terms: 0 + -312.5 = -312.5 -67.1666875t + t2 = -312.5 The t term is -67.1666875t. Take half its coefficient (-33.58334375). Square it (1127.840977) and add it to both sides. Add '1127.840977' to each side of the equation. -67.1666875t + 1127.840977 + t2 = -312.5 + 1127.840977 Reorder the terms: 1127.840977 + -67.1666875t + t2 = -312.5 + 1127.840977 Combine like terms: -312.5 + 1127.840977 = 815.340977 1127.840977 + -67.1666875t + t2 = 815.340977 Factor a perfect square on the left side: (t + -33.58334375)(t + -33.58334375) = 815.340977 Calculate the square root of the right side: 28.554176174 Break this problem into two subproblems by setting (t + -33.58334375) equal to 28.554176174 and -28.554176174.Subproblem 1
t + -33.58334375 = 28.554176174 Simplifying t + -33.58334375 = 28.554176174 Reorder the terms: -33.58334375 + t = 28.554176174 Solving -33.58334375 + t = 28.554176174 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '33.58334375' to each side of the equation. -33.58334375 + 33.58334375 + t = 28.554176174 + 33.58334375 Combine like terms: -33.58334375 + 33.58334375 = 0.00000000 0.00000000 + t = 28.554176174 + 33.58334375 t = 28.554176174 + 33.58334375 Combine like terms: 28.554176174 + 33.58334375 = 62.137519924 t = 62.137519924 Simplifying t = 62.137519924Subproblem 2
t + -33.58334375 = -28.554176174 Simplifying t + -33.58334375 = -28.554176174 Reorder the terms: -33.58334375 + t = -28.554176174 Solving -33.58334375 + t = -28.554176174 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '33.58334375' to each side of the equation. -33.58334375 + 33.58334375 + t = -28.554176174 + 33.58334375 Combine like terms: -33.58334375 + 33.58334375 = 0.00000000 0.00000000 + t = -28.554176174 + 33.58334375 t = -28.554176174 + 33.58334375 Combine like terms: -28.554176174 + 33.58334375 = 5.029167576 t = 5.029167576 Simplifying t = 5.029167576Solution
The solution to the problem is based on the solutions from the subproblems. t = {62.137519924, 5.029167576}
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