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Simplifying 8t2 + 16t + 5 = 0 Reorder the terms: 5 + 16t + 8t2 = 0 Solving 5 + 16t + 8t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.625 + 2t + t2 = 0 Move the constant term to the right: Add '-0.625' to each side of the equation. 0.625 + 2t + -0.625 + t2 = 0 + -0.625 Reorder the terms: 0.625 + -0.625 + 2t + t2 = 0 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + 2t + t2 = 0 + -0.625 2t + t2 = 0 + -0.625 Combine like terms: 0 + -0.625 = -0.625 2t + t2 = -0.625 The t term is 2t. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2t + 1 + t2 = -0.625 + 1 Reorder the terms: 1 + 2t + t2 = -0.625 + 1 Combine like terms: -0.625 + 1 = 0.375 1 + 2t + t2 = 0.375 Factor a perfect square on the left side: (t + 1)(t + 1) = 0.375 Calculate the square root of the right side: 0.612372436 Break this problem into two subproblems by setting (t + 1) equal to 0.612372436 and -0.612372436.Subproblem 1
t + 1 = 0.612372436 Simplifying t + 1 = 0.612372436 Reorder the terms: 1 + t = 0.612372436 Solving 1 + t = 0.612372436 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + t = 0.612372436 + -1 Combine like terms: 1 + -1 = 0 0 + t = 0.612372436 + -1 t = 0.612372436 + -1 Combine like terms: 0.612372436 + -1 = -0.387627564 t = -0.387627564 Simplifying t = -0.387627564Subproblem 2
t + 1 = -0.612372436 Simplifying t + 1 = -0.612372436 Reorder the terms: 1 + t = -0.612372436 Solving 1 + t = -0.612372436 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + t = -0.612372436 + -1 Combine like terms: 1 + -1 = 0 0 + t = -0.612372436 + -1 t = -0.612372436 + -1 Combine like terms: -0.612372436 + -1 = -1.612372436 t = -1.612372436 Simplifying t = -1.612372436Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.387627564, -1.612372436}
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