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Simplifying 4.9t2 + 5t + -30 = 0 Reorder the terms: -30 + 5t + 4.9t2 = 0 Solving -30 + 5t + 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'. -6.12244898 + 1.020408163t + t2 = 0 Move the constant term to the right: Add '6.12244898' to each side of the equation. -6.12244898 + 1.020408163t + 6.12244898 + t2 = 0 + 6.12244898 Reorder the terms: -6.12244898 + 6.12244898 + 1.020408163t + t2 = 0 + 6.12244898 Combine like terms: -6.12244898 + 6.12244898 = 0.00000000 0.00000000 + 1.020408163t + t2 = 0 + 6.12244898 1.020408163t + t2 = 0 + 6.12244898 Combine like terms: 0 + 6.12244898 = 6.12244898 1.020408163t + t2 = 6.12244898 The t term is 1.020408163t. Take half its coefficient (0.5102040815). Square it (0.2603082048) and add it to both sides. Add '0.2603082048' to each side of the equation. 1.020408163t + 0.2603082048 + t2 = 6.12244898 + 0.2603082048 Reorder the terms: 0.2603082048 + 1.020408163t + t2 = 6.12244898 + 0.2603082048 Combine like terms: 6.12244898 + 0.2603082048 = 6.3827571848 0.2603082048 + 1.020408163t + t2 = 6.3827571848 Factor a perfect square on the left side: (t + 0.5102040815)(t + 0.5102040815) = 6.3827571848 Calculate the square root of the right side: 2.526411919 Break this problem into two subproblems by setting (t + 0.5102040815) equal to 2.526411919 and -2.526411919.Subproblem 1
t + 0.5102040815 = 2.526411919 Simplifying t + 0.5102040815 = 2.526411919 Reorder the terms: 0.5102040815 + t = 2.526411919 Solving 0.5102040815 + t = 2.526411919 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5102040815' to each side of the equation. 0.5102040815 + -0.5102040815 + t = 2.526411919 + -0.5102040815 Combine like terms: 0.5102040815 + -0.5102040815 = 0.0000000000 0.0000000000 + t = 2.526411919 + -0.5102040815 t = 2.526411919 + -0.5102040815 Combine like terms: 2.526411919 + -0.5102040815 = 2.0162078375 t = 2.0162078375 Simplifying t = 2.0162078375Subproblem 2
t + 0.5102040815 = -2.526411919 Simplifying t + 0.5102040815 = -2.526411919 Reorder the terms: 0.5102040815 + t = -2.526411919 Solving 0.5102040815 + t = -2.526411919 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5102040815' to each side of the equation. 0.5102040815 + -0.5102040815 + t = -2.526411919 + -0.5102040815 Combine like terms: 0.5102040815 + -0.5102040815 = 0.0000000000 0.0000000000 + t = -2.526411919 + -0.5102040815 t = -2.526411919 + -0.5102040815 Combine like terms: -2.526411919 + -0.5102040815 = -3.0366160005 t = -3.0366160005 Simplifying t = -3.0366160005Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.0162078375, -3.0366160005}
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