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Simplifying 8t2 + 22t + -5 = 0 Reorder the terms: -5 + 22t + 8t2 = 0 Solving -5 + 22t + 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 + 2.75t + t2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + 2.75t + 0.625 + t2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + 2.75t + t2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + 2.75t + t2 = 0 + 0.625 2.75t + t2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 2.75t + t2 = 0.625 The t term is 2.75t. Take half its coefficient (1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. 2.75t + 1.890625 + t2 = 0.625 + 1.890625 Reorder the terms: 1.890625 + 2.75t + t2 = 0.625 + 1.890625 Combine like terms: 0.625 + 1.890625 = 2.515625 1.890625 + 2.75t + t2 = 2.515625 Factor a perfect square on the left side: (t + 1.375)(t + 1.375) = 2.515625 Calculate the square root of the right side: 1.586072193 Break this problem into two subproblems by setting (t + 1.375) equal to 1.586072193 and -1.586072193.Subproblem 1
t + 1.375 = 1.586072193 Simplifying t + 1.375 = 1.586072193 Reorder the terms: 1.375 + t = 1.586072193 Solving 1.375 + t = 1.586072193 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.375' to each side of the equation. 1.375 + -1.375 + t = 1.586072193 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + t = 1.586072193 + -1.375 t = 1.586072193 + -1.375 Combine like terms: 1.586072193 + -1.375 = 0.211072193 t = 0.211072193 Simplifying t = 0.211072193Subproblem 2
t + 1.375 = -1.586072193 Simplifying t + 1.375 = -1.586072193 Reorder the terms: 1.375 + t = -1.586072193 Solving 1.375 + t = -1.586072193 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.375' to each side of the equation. 1.375 + -1.375 + t = -1.586072193 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + t = -1.586072193 + -1.375 t = -1.586072193 + -1.375 Combine like terms: -1.586072193 + -1.375 = -2.961072193 t = -2.961072193 Simplifying t = -2.961072193Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.211072193, -2.961072193}
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