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Simplifying 0 = -16t2 + 131t + 84 Reorder the terms: 0 = 84 + 131t + -16t2 Solving 0 = 84 + 131t + -16t2 Solving for variable 't'. Combine like terms: 0 + -84 = -84 -84 + -131t + 16t2 = 84 + 131t + -16t2 + -84 + -131t + 16t2 Reorder the terms: -84 + -131t + 16t2 = 84 + -84 + 131t + -131t + -16t2 + 16t2 Combine like terms: 84 + -84 = 0 -84 + -131t + 16t2 = 0 + 131t + -131t + -16t2 + 16t2 -84 + -131t + 16t2 = 131t + -131t + -16t2 + 16t2 Combine like terms: 131t + -131t = 0 -84 + -131t + 16t2 = 0 + -16t2 + 16t2 -84 + -131t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -84 + -131t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -5.25 + -8.1875t + t2 = 0 Move the constant term to the right: Add '5.25' to each side of the equation. -5.25 + -8.1875t + 5.25 + t2 = 0 + 5.25 Reorder the terms: -5.25 + 5.25 + -8.1875t + t2 = 0 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + -8.1875t + t2 = 0 + 5.25 -8.1875t + t2 = 0 + 5.25 Combine like terms: 0 + 5.25 = 5.25 -8.1875t + t2 = 5.25 The t term is -8.1875t. Take half its coefficient (-4.09375). Square it (16.75878906) and add it to both sides. Add '16.75878906' to each side of the equation. -8.1875t + 16.75878906 + t2 = 5.25 + 16.75878906 Reorder the terms: 16.75878906 + -8.1875t + t2 = 5.25 + 16.75878906 Combine like terms: 5.25 + 16.75878906 = 22.00878906 16.75878906 + -8.1875t + t2 = 22.00878906 Factor a perfect square on the left side: (t + -4.09375)(t + -4.09375) = 22.00878906 Calculate the square root of the right side: 4.691352583 Break this problem into two subproblems by setting (t + -4.09375) equal to 4.691352583 and -4.691352583.Subproblem 1
t + -4.09375 = 4.691352583 Simplifying t + -4.09375 = 4.691352583 Reorder the terms: -4.09375 + t = 4.691352583 Solving -4.09375 + t = 4.691352583 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.09375' to each side of the equation. -4.09375 + 4.09375 + t = 4.691352583 + 4.09375 Combine like terms: -4.09375 + 4.09375 = 0.00000 0.00000 + t = 4.691352583 + 4.09375 t = 4.691352583 + 4.09375 Combine like terms: 4.691352583 + 4.09375 = 8.785102583 t = 8.785102583 Simplifying t = 8.785102583Subproblem 2
t + -4.09375 = -4.691352583 Simplifying t + -4.09375 = -4.691352583 Reorder the terms: -4.09375 + t = -4.691352583 Solving -4.09375 + t = -4.691352583 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.09375' to each side of the equation. -4.09375 + 4.09375 + t = -4.691352583 + 4.09375 Combine like terms: -4.09375 + 4.09375 = 0.00000 0.00000 + t = -4.691352583 + 4.09375 t = -4.691352583 + 4.09375 Combine like terms: -4.691352583 + 4.09375 = -0.597602583 t = -0.597602583 Simplifying t = -0.597602583Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.785102583, -0.597602583}
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