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Simplifying -16t2 + 36 = -65t Reorder the terms: 36 + -16t2 = -65t Solving 36 + -16t2 = -65t Solving for variable 't'. Reorder the terms: 36 + 65t + -16t2 = -65t + 65t Combine like terms: -65t + 65t = 0 36 + 65t + -16t2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -2.25 + -4.0625t + t2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + -4.0625t + 2.25 + t2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + -4.0625t + t2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + -4.0625t + t2 = 0 + 2.25 -4.0625t + t2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 -4.0625t + t2 = 2.25 The t term is -4.0625t. Take half its coefficient (-2.03125). Square it (4.125976563) and add it to both sides. Add '4.125976563' to each side of the equation. -4.0625t + 4.125976563 + t2 = 2.25 + 4.125976563 Reorder the terms: 4.125976563 + -4.0625t + t2 = 2.25 + 4.125976563 Combine like terms: 2.25 + 4.125976563 = 6.375976563 4.125976563 + -4.0625t + t2 = 6.375976563 Factor a perfect square on the left side: (t + -2.03125)(t + -2.03125) = 6.375976563 Calculate the square root of the right side: 2.525069615 Break this problem into two subproblems by setting (t + -2.03125) equal to 2.525069615 and -2.525069615.Subproblem 1
t + -2.03125 = 2.525069615 Simplifying t + -2.03125 = 2.525069615 Reorder the terms: -2.03125 + t = 2.525069615 Solving -2.03125 + t = 2.525069615 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.03125' to each side of the equation. -2.03125 + 2.03125 + t = 2.525069615 + 2.03125 Combine like terms: -2.03125 + 2.03125 = 0.00000 0.00000 + t = 2.525069615 + 2.03125 t = 2.525069615 + 2.03125 Combine like terms: 2.525069615 + 2.03125 = 4.556319615 t = 4.556319615 Simplifying t = 4.556319615Subproblem 2
t + -2.03125 = -2.525069615 Simplifying t + -2.03125 = -2.525069615 Reorder the terms: -2.03125 + t = -2.525069615 Solving -2.03125 + t = -2.525069615 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.03125' to each side of the equation. -2.03125 + 2.03125 + t = -2.525069615 + 2.03125 Combine like terms: -2.03125 + 2.03125 = 0.00000 0.00000 + t = -2.525069615 + 2.03125 t = -2.525069615 + 2.03125 Combine like terms: -2.525069615 + 2.03125 = -0.493819615 t = -0.493819615 Simplifying t = -0.493819615Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.556319615, -0.493819615}
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