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Simplifying 80t + -16t2 + 35 = 0 Reorder the terms: 35 + 80t + -16t2 = 0 Solving 35 + 80t + -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'. -2.1875 + -5t + t2 = 0 Move the constant term to the right: Add '2.1875' to each side of the equation. -2.1875 + -5t + 2.1875 + t2 = 0 + 2.1875 Reorder the terms: -2.1875 + 2.1875 + -5t + t2 = 0 + 2.1875 Combine like terms: -2.1875 + 2.1875 = 0.0000 0.0000 + -5t + t2 = 0 + 2.1875 -5t + t2 = 0 + 2.1875 Combine like terms: 0 + 2.1875 = 2.1875 -5t + t2 = 2.1875 The t term is -5t. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5t + 6.25 + t2 = 2.1875 + 6.25 Reorder the terms: 6.25 + -5t + t2 = 2.1875 + 6.25 Combine like terms: 2.1875 + 6.25 = 8.4375 6.25 + -5t + t2 = 8.4375 Factor a perfect square on the left side: (t + -2.5)(t + -2.5) = 8.4375 Calculate the square root of the right side: 2.90473751 Break this problem into two subproblems by setting (t + -2.5) equal to 2.90473751 and -2.90473751.Subproblem 1
t + -2.5 = 2.90473751 Simplifying t + -2.5 = 2.90473751 Reorder the terms: -2.5 + t = 2.90473751 Solving -2.5 + t = 2.90473751 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + t = 2.90473751 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = 2.90473751 + 2.5 t = 2.90473751 + 2.5 Combine like terms: 2.90473751 + 2.5 = 5.40473751 t = 5.40473751 Simplifying t = 5.40473751Subproblem 2
t + -2.5 = -2.90473751 Simplifying t + -2.5 = -2.90473751 Reorder the terms: -2.5 + t = -2.90473751 Solving -2.5 + t = -2.90473751 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + t = -2.90473751 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = -2.90473751 + 2.5 t = -2.90473751 + 2.5 Combine like terms: -2.90473751 + 2.5 = -0.40473751 t = -0.40473751 Simplifying t = -0.40473751Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.40473751, -0.40473751}
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