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Simplifying -4.9t2 + 33.6t + 4.9 = 0 Reorder the terms: 4.9 + 33.6t + -4.9t2 = 0 Solving 4.9 + 33.6t + -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'. -1 + -6.857142857t + t2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -6.857142857t + 1 + t2 = 0 + 1 Reorder the terms: -1 + 1 + -6.857142857t + t2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -6.857142857t + t2 = 0 + 1 -6.857142857t + t2 = 0 + 1 Combine like terms: 0 + 1 = 1 -6.857142857t + t2 = 1 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 = 1 + 11.75510204 Reorder the terms: 11.75510204 + -6.857142857t + t2 = 1 + 11.75510204 Combine like terms: 1 + 11.75510204 = 12.75510204 11.75510204 + -6.857142857t + t2 = 12.75510204 Factor a perfect square on the left side: (t + -3.428571429)(t + -3.428571429) = 12.75510204 Calculate the square root of the right side: 3.571428571 Break this problem into two subproblems by setting (t + -3.428571429) equal to 3.571428571 and -3.571428571.Subproblem 1
t + -3.428571429 = 3.571428571 Simplifying t + -3.428571429 = 3.571428571 Reorder the terms: -3.428571429 + t = 3.571428571 Solving -3.428571429 + t = 3.571428571 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 = 3.571428571 + 3.428571429 Combine like terms: -3.428571429 + 3.428571429 = 0.000000000 0.000000000 + t = 3.571428571 + 3.428571429 t = 3.571428571 + 3.428571429 Combine like terms: 3.571428571 + 3.428571429 = 7 t = 7 Simplifying t = 7Subproblem 2
t + -3.428571429 = -3.571428571 Simplifying t + -3.428571429 = -3.571428571 Reorder the terms: -3.428571429 + t = -3.571428571 Solving -3.428571429 + t = -3.571428571 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 = -3.571428571 + 3.428571429 Combine like terms: -3.428571429 + 3.428571429 = 0.000000000 0.000000000 + t = -3.571428571 + 3.428571429 t = -3.571428571 + 3.428571429 Combine like terms: -3.571428571 + 3.428571429 = -0.142857142 t = -0.142857142 Simplifying t = -0.142857142Solution
The solution to the problem is based on the solutions from the subproblems. t = {7, -0.142857142}
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