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Simplifying t = 4.9t2 + 27t + 9.8 Reorder the terms: t = 9.8 + 27t + 4.9t2 Solving t = 9.8 + 27t + 4.9t2 Solving for variable 't'. Reorder the terms: -9.8 + t + -27t + -4.9t2 = 9.8 + 27t + 4.9t2 + -9.8 + -27t + -4.9t2 Combine like terms: t + -27t = -26t -9.8 + -26t + -4.9t2 = 9.8 + 27t + 4.9t2 + -9.8 + -27t + -4.9t2 Reorder the terms: -9.8 + -26t + -4.9t2 = 9.8 + -9.8 + 27t + -27t + 4.9t2 + -4.9t2 Combine like terms: 9.8 + -9.8 = 0.0 -9.8 + -26t + -4.9t2 = 0.0 + 27t + -27t + 4.9t2 + -4.9t2 -9.8 + -26t + -4.9t2 = 27t + -27t + 4.9t2 + -4.9t2 Combine like terms: 27t + -27t = 0 -9.8 + -26t + -4.9t2 = 0 + 4.9t2 + -4.9t2 -9.8 + -26t + -4.9t2 = 4.9t2 + -4.9t2 Combine like terms: 4.9t2 + -4.9t2 = 0.0 -9.8 + -26t + -4.9t2 = 0.0 Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. 2 + 5.306122449t + t2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + 5.306122449t + -2 + t2 = 0 + -2 Reorder the terms: 2 + -2 + 5.306122449t + t2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 5.306122449t + t2 = 0 + -2 5.306122449t + t2 = 0 + -2 Combine like terms: 0 + -2 = -2 5.306122449t + t2 = -2 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 + 7.038733864 Reorder the terms: 7.038733864 + 5.306122449t + t2 = -2 + 7.038733864 Combine like terms: -2 + 7.038733864 = 5.038733864 7.038733864 + 5.306122449t + t2 = 5.038733864 Factor a perfect square on the left side: (t + 2.653061225)(t + 2.653061225) = 5.038733864 Calculate the square root of the right side: 2.244712423 Break this problem into two subproblems by setting (t + 2.653061225) equal to 2.244712423 and -2.244712423.Subproblem 1
t + 2.653061225 = 2.244712423 Simplifying t + 2.653061225 = 2.244712423 Reorder the terms: 2.653061225 + t = 2.244712423 Solving 2.653061225 + t = 2.244712423 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 = 2.244712423 + -2.653061225 Combine like terms: 2.653061225 + -2.653061225 = 0.000000000 0.000000000 + t = 2.244712423 + -2.653061225 t = 2.244712423 + -2.653061225 Combine like terms: 2.244712423 + -2.653061225 = -0.408348802 t = -0.408348802 Simplifying t = -0.408348802Subproblem 2
t + 2.653061225 = -2.244712423 Simplifying t + 2.653061225 = -2.244712423 Reorder the terms: 2.653061225 + t = -2.244712423 Solving 2.653061225 + t = -2.244712423 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 = -2.244712423 + -2.653061225 Combine like terms: 2.653061225 + -2.653061225 = 0.000000000 0.000000000 + t = -2.244712423 + -2.653061225 t = -2.244712423 + -2.653061225 Combine like terms: -2.244712423 + -2.653061225 = -4.897773648 t = -4.897773648 Simplifying t = -4.897773648Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.408348802, -4.897773648}
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