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Simplifying -16t2 + 105t = 63.2 Reorder the terms: 105t + -16t2 = 63.2 Solving 105t + -16t2 = 63.2 Solving for variable 't'. Reorder the terms: -63.2 + 105t + -16t2 = 63.2 + -63.2 Combine like terms: 63.2 + -63.2 = 0.0 -63.2 + 105t + -16t2 = 0.0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. 3.95 + -6.5625t + t2 = 0.0 Move the constant term to the right: Add '-3.95' to each side of the equation. 3.95 + -6.5625t + -3.95 + t2 = 0.0 + -3.95 Reorder the terms: 3.95 + -3.95 + -6.5625t + t2 = 0.0 + -3.95 Combine like terms: 3.95 + -3.95 = 0.00 0.00 + -6.5625t + t2 = 0.0 + -3.95 -6.5625t + t2 = 0.0 + -3.95 Combine like terms: 0.0 + -3.95 = -3.95 -6.5625t + t2 = -3.95 The t term is -6.5625t. Take half its coefficient (-3.28125). Square it (10.76660156) and add it to both sides. Add '10.76660156' to each side of the equation. -6.5625t + 10.76660156 + t2 = -3.95 + 10.76660156 Reorder the terms: 10.76660156 + -6.5625t + t2 = -3.95 + 10.76660156 Combine like terms: -3.95 + 10.76660156 = 6.81660156 10.76660156 + -6.5625t + t2 = 6.81660156 Factor a perfect square on the left side: (t + -3.28125)(t + -3.28125) = 6.81660156 Calculate the square root of the right side: 2.610862225 Break this problem into two subproblems by setting (t + -3.28125) equal to 2.610862225 and -2.610862225.Subproblem 1
t + -3.28125 = 2.610862225 Simplifying t + -3.28125 = 2.610862225 Reorder the terms: -3.28125 + t = 2.610862225 Solving -3.28125 + t = 2.610862225 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.28125' to each side of the equation. -3.28125 + 3.28125 + t = 2.610862225 + 3.28125 Combine like terms: -3.28125 + 3.28125 = 0.00000 0.00000 + t = 2.610862225 + 3.28125 t = 2.610862225 + 3.28125 Combine like terms: 2.610862225 + 3.28125 = 5.892112225 t = 5.892112225 Simplifying t = 5.892112225Subproblem 2
t + -3.28125 = -2.610862225 Simplifying t + -3.28125 = -2.610862225 Reorder the terms: -3.28125 + t = -2.610862225 Solving -3.28125 + t = -2.610862225 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.28125' to each side of the equation. -3.28125 + 3.28125 + t = -2.610862225 + 3.28125 Combine like terms: -3.28125 + 3.28125 = 0.00000 0.00000 + t = -2.610862225 + 3.28125 t = -2.610862225 + 3.28125 Combine like terms: -2.610862225 + 3.28125 = 0.670387775 t = 0.670387775 Simplifying t = 0.670387775Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.892112225, 0.670387775}
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