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Simplifying 4.9t2 + -26t + -10 = 0 Reorder the terms: -10 + -26t + 4.9t2 = 0 Solving -10 + -26t + 4.9t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -2.040816327 + -5.306122449t + t2 = 0 Move the constant term to the right: Add '2.040816327' to each side of the equation. -2.040816327 + -5.306122449t + 2.040816327 + t2 = 0 + 2.040816327 Reorder the terms: -2.040816327 + 2.040816327 + -5.306122449t + t2 = 0 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + -5.306122449t + t2 = 0 + 2.040816327 -5.306122449t + t2 = 0 + 2.040816327 Combine like terms: 0 + 2.040816327 = 2.040816327 -5.306122449t + t2 = 2.040816327 The t term is -5.306122449t. Take half its coefficient (-2.653061225). Square it (7.038733864) and add it to both sides. Add '7.038733864' to each side of the equation. -5.306122449t + 7.038733864 + t2 = 2.040816327 + 7.038733864 Reorder the terms: 7.038733864 + -5.306122449t + t2 = 2.040816327 + 7.038733864 Combine like terms: 2.040816327 + 7.038733864 = 9.079550191 7.038733864 + -5.306122449t + t2 = 9.079550191 Factor a perfect square on the left side: (t + -2.653061225)(t + -2.653061225) = 9.079550191 Calculate the square root of the right side: 3.013229197 Break this problem into two subproblems by setting (t + -2.653061225) equal to 3.013229197 and -3.013229197.Subproblem 1
t + -2.653061225 = 3.013229197 Simplifying t + -2.653061225 = 3.013229197 Reorder the terms: -2.653061225 + t = 3.013229197 Solving -2.653061225 + t = 3.013229197 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.653061225' to each side of the equation. -2.653061225 + 2.653061225 + t = 3.013229197 + 2.653061225 Combine like terms: -2.653061225 + 2.653061225 = 0.000000000 0.000000000 + t = 3.013229197 + 2.653061225 t = 3.013229197 + 2.653061225 Combine like terms: 3.013229197 + 2.653061225 = 5.666290422 t = 5.666290422 Simplifying t = 5.666290422Subproblem 2
t + -2.653061225 = -3.013229197 Simplifying t + -2.653061225 = -3.013229197 Reorder the terms: -2.653061225 + t = -3.013229197 Solving -2.653061225 + t = -3.013229197 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.653061225' to each side of the equation. -2.653061225 + 2.653061225 + t = -3.013229197 + 2.653061225 Combine like terms: -2.653061225 + 2.653061225 = 0.000000000 0.000000000 + t = -3.013229197 + 2.653061225 t = -3.013229197 + 2.653061225 Combine like terms: -3.013229197 + 2.653061225 = -0.360167972 t = -0.360167972 Simplifying t = -0.360167972Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.666290422, -0.360167972}
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