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Simplifying -16t2 + 128t + 16.25 = 0 Reorder the terms: 16.25 + 128t + -16t2 = 0 Solving 16.25 + 128t + -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'. -1.015625 + -8t + t2 = 0 Move the constant term to the right: Add '1.015625' to each side of the equation. -1.015625 + -8t + 1.015625 + t2 = 0 + 1.015625 Reorder the terms: -1.015625 + 1.015625 + -8t + t2 = 0 + 1.015625 Combine like terms: -1.015625 + 1.015625 = 0.000000 0.000000 + -8t + t2 = 0 + 1.015625 -8t + t2 = 0 + 1.015625 Combine like terms: 0 + 1.015625 = 1.015625 -8t + t2 = 1.015625 The t term is -8t. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8t + 16 + t2 = 1.015625 + 16 Reorder the terms: 16 + -8t + t2 = 1.015625 + 16 Combine like terms: 1.015625 + 16 = 17.015625 16 + -8t + t2 = 17.015625 Factor a perfect square on the left side: (t + -4)(t + -4) = 17.015625 Calculate the square root of the right side: 4.125 Break this problem into two subproblems by setting (t + -4) equal to 4.125 and -4.125.Subproblem 1
t + -4 = 4.125 Simplifying t + -4 = 4.125 Reorder the terms: -4 + t = 4.125 Solving -4 + t = 4.125 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = 4.125 + 4 Combine like terms: -4 + 4 = 0 0 + t = 4.125 + 4 t = 4.125 + 4 Combine like terms: 4.125 + 4 = 8.125 t = 8.125 Simplifying t = 8.125Subproblem 2
t + -4 = -4.125 Simplifying t + -4 = -4.125 Reorder the terms: -4 + t = -4.125 Solving -4 + t = -4.125 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = -4.125 + 4 Combine like terms: -4 + 4 = 0 0 + t = -4.125 + 4 t = -4.125 + 4 Combine like terms: -4.125 + 4 = -0.125 t = -0.125 Simplifying t = -0.125Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.125, -0.125}
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