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Simplifying 4 = 16t2 + 129t Reorder the terms: 4 = 129t + 16t2 Solving 4 = 129t + 16t2 Solving for variable 't'. Reorder the terms: 4 + -129t + -16t2 = 129t + -129t + 16t2 + -16t2 Combine like terms: 129t + -129t = 0 4 + -129t + -16t2 = 0 + 16t2 + -16t2 4 + -129t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 4 + -129t + -16t2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.25 + 8.0625t + t2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + 8.0625t + 0.25 + t2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + 8.0625t + t2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + 8.0625t + t2 = 0 + 0.25 8.0625t + t2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 8.0625t + t2 = 0.25 The t term is 8.0625t. Take half its coefficient (4.03125). Square it (16.25097656) and add it to both sides. Add '16.25097656' to each side of the equation. 8.0625t + 16.25097656 + t2 = 0.25 + 16.25097656 Reorder the terms: 16.25097656 + 8.0625t + t2 = 0.25 + 16.25097656 Combine like terms: 0.25 + 16.25097656 = 16.50097656 16.25097656 + 8.0625t + t2 = 16.50097656 Factor a perfect square on the left side: (t + 4.03125)(t + 4.03125) = 16.50097656 Calculate the square root of the right side: 4.062139407 Break this problem into two subproblems by setting (t + 4.03125) equal to 4.062139407 and -4.062139407.Subproblem 1
t + 4.03125 = 4.062139407 Simplifying t + 4.03125 = 4.062139407 Reorder the terms: 4.03125 + t = 4.062139407 Solving 4.03125 + t = 4.062139407 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-4.03125' to each side of the equation. 4.03125 + -4.03125 + t = 4.062139407 + -4.03125 Combine like terms: 4.03125 + -4.03125 = 0.00000 0.00000 + t = 4.062139407 + -4.03125 t = 4.062139407 + -4.03125 Combine like terms: 4.062139407 + -4.03125 = 0.030889407 t = 0.030889407 Simplifying t = 0.030889407Subproblem 2
t + 4.03125 = -4.062139407 Simplifying t + 4.03125 = -4.062139407 Reorder the terms: 4.03125 + t = -4.062139407 Solving 4.03125 + t = -4.062139407 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-4.03125' to each side of the equation. 4.03125 + -4.03125 + t = -4.062139407 + -4.03125 Combine like terms: 4.03125 + -4.03125 = 0.00000 0.00000 + t = -4.062139407 + -4.03125 t = -4.062139407 + -4.03125 Combine like terms: -4.062139407 + -4.03125 = -8.093389407 t = -8.093389407 Simplifying t = -8.093389407Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.030889407, -8.093389407}
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