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Simplifying 0 = -4.9t2 + 33.6t + 49 Reorder the terms: 0 = 49 + 33.6t + -4.9t2 Solving 0 = 49 + 33.6t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -49 = -49 -49 + -33.6t + 4.9t2 = 49 + 33.6t + -4.9t2 + -49 + -33.6t + 4.9t2 Reorder the terms: -49 + -33.6t + 4.9t2 = 49 + -49 + 33.6t + -33.6t + -4.9t2 + 4.9t2 Combine like terms: 49 + -49 = 0 -49 + -33.6t + 4.9t2 = 0 + 33.6t + -33.6t + -4.9t2 + 4.9t2 -49 + -33.6t + 4.9t2 = 33.6t + -33.6t + -4.9t2 + 4.9t2 Combine like terms: 33.6t + -33.6t = 0.0 -49 + -33.6t + 4.9t2 = 0.0 + -4.9t2 + 4.9t2 -49 + -33.6t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -49 + -33.6t + 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'. -10 + -6.857142857t + t2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -6.857142857t + 10 + t2 = 0 + 10 Reorder the terms: -10 + 10 + -6.857142857t + t2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -6.857142857t + t2 = 0 + 10 -6.857142857t + t2 = 0 + 10 Combine like terms: 0 + 10 = 10 -6.857142857t + t2 = 10 The t term is -6.857142857t. Take half its coefficient (-3.428571429). Square it (11.75510204) and add it to both sides. Add '11.75510204' to each side of the equation. -6.857142857t + 11.75510204 + t2 = 10 + 11.75510204 Reorder the terms: 11.75510204 + -6.857142857t + t2 = 10 + 11.75510204 Combine like terms: 10 + 11.75510204 = 21.75510204 11.75510204 + -6.857142857t + t2 = 21.75510204 Factor a perfect square on the left side: (t + -3.428571429)(t + -3.428571429) = 21.75510204 Calculate the square root of the right side: 4.664236491 Break this problem into two subproblems by setting (t + -3.428571429) equal to 4.664236491 and -4.664236491.Subproblem 1
t + -3.428571429 = 4.664236491 Simplifying t + -3.428571429 = 4.664236491 Reorder the terms: -3.428571429 + t = 4.664236491 Solving -3.428571429 + t = 4.664236491 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.428571429' to each side of the equation. -3.428571429 + 3.428571429 + t = 4.664236491 + 3.428571429 Combine like terms: -3.428571429 + 3.428571429 = 0.000000000 0.000000000 + t = 4.664236491 + 3.428571429 t = 4.664236491 + 3.428571429 Combine like terms: 4.664236491 + 3.428571429 = 8.09280792 t = 8.09280792 Simplifying t = 8.09280792Subproblem 2
t + -3.428571429 = -4.664236491 Simplifying t + -3.428571429 = -4.664236491 Reorder the terms: -3.428571429 + t = -4.664236491 Solving -3.428571429 + t = -4.664236491 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.428571429' to each side of the equation. -3.428571429 + 3.428571429 + t = -4.664236491 + 3.428571429 Combine like terms: -3.428571429 + 3.428571429 = 0.000000000 0.000000000 + t = -4.664236491 + 3.428571429 t = -4.664236491 + 3.428571429 Combine like terms: -4.664236491 + 3.428571429 = -1.235665062 t = -1.235665062 Simplifying t = -1.235665062Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.09280792, -1.235665062}
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