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Simplifying 2t2 + 17t + -8 = 0 Reorder the terms: -8 + 17t + 2t2 = 0 Solving -8 + 17t + 2t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -4 + 8.5t + t2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 8.5t + 4 + t2 = 0 + 4 Reorder the terms: -4 + 4 + 8.5t + t2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 8.5t + t2 = 0 + 4 8.5t + t2 = 0 + 4 Combine like terms: 0 + 4 = 4 8.5t + t2 = 4 The t term is 8.5t. Take half its coefficient (4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. 8.5t + 18.0625 + t2 = 4 + 18.0625 Reorder the terms: 18.0625 + 8.5t + t2 = 4 + 18.0625 Combine like terms: 4 + 18.0625 = 22.0625 18.0625 + 8.5t + t2 = 22.0625 Factor a perfect square on the left side: (t + 4.25)(t + 4.25) = 22.0625 Calculate the square root of the right side: 4.697073557 Break this problem into two subproblems by setting (t + 4.25) equal to 4.697073557 and -4.697073557.Subproblem 1
t + 4.25 = 4.697073557 Simplifying t + 4.25 = 4.697073557 Reorder the terms: 4.25 + t = 4.697073557 Solving 4.25 + t = 4.697073557 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + t = 4.697073557 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + t = 4.697073557 + -4.25 t = 4.697073557 + -4.25 Combine like terms: 4.697073557 + -4.25 = 0.447073557 t = 0.447073557 Simplifying t = 0.447073557Subproblem 2
t + 4.25 = -4.697073557 Simplifying t + 4.25 = -4.697073557 Reorder the terms: 4.25 + t = -4.697073557 Solving 4.25 + t = -4.697073557 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + t = -4.697073557 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + t = -4.697073557 + -4.25 t = -4.697073557 + -4.25 Combine like terms: -4.697073557 + -4.25 = -8.947073557 t = -8.947073557 Simplifying t = -8.947073557Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.447073557, -8.947073557}
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