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Simplifying -4.9t2 + t + 360 = -4t + 142 Reorder the terms: 360 + t + -4.9t2 = -4t + 142 Reorder the terms: 360 + t + -4.9t2 = 142 + -4t Solving 360 + t + -4.9t2 = 142 + -4t Solving for variable 't'. Reorder the terms: 360 + -142 + t + 4t + -4.9t2 = 142 + -4t + -142 + 4t Combine like terms: 360 + -142 = 218 218 + t + 4t + -4.9t2 = 142 + -4t + -142 + 4t Combine like terms: t + 4t = 5t 218 + 5t + -4.9t2 = 142 + -4t + -142 + 4t Reorder the terms: 218 + 5t + -4.9t2 = 142 + -142 + -4t + 4t Combine like terms: 142 + -142 = 0 218 + 5t + -4.9t2 = 0 + -4t + 4t 218 + 5t + -4.9t2 = -4t + 4t Combine like terms: -4t + 4t = 0 218 + 5t + -4.9t2 = 0 Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -44.48979592 + -1.020408163t + t2 = 0 Move the constant term to the right: Add '44.48979592' to each side of the equation. -44.48979592 + -1.020408163t + 44.48979592 + t2 = 0 + 44.48979592 Reorder the terms: -44.48979592 + 44.48979592 + -1.020408163t + t2 = 0 + 44.48979592 Combine like terms: -44.48979592 + 44.48979592 = 0.00000000 0.00000000 + -1.020408163t + t2 = 0 + 44.48979592 -1.020408163t + t2 = 0 + 44.48979592 Combine like terms: 0 + 44.48979592 = 44.48979592 -1.020408163t + t2 = 44.48979592 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 = 44.48979592 + 0.2603082048 Reorder the terms: 0.2603082048 + -1.020408163t + t2 = 44.48979592 + 0.2603082048 Combine like terms: 44.48979592 + 0.2603082048 = 44.7501041248 0.2603082048 + -1.020408163t + t2 = 44.7501041248 Factor a perfect square on the left side: (t + -0.5102040815)(t + -0.5102040815) = 44.7501041248 Calculate the square root of the right side: 6.689551863 Break this problem into two subproblems by setting (t + -0.5102040815) equal to 6.689551863 and -6.689551863.Subproblem 1
t + -0.5102040815 = 6.689551863 Simplifying t + -0.5102040815 = 6.689551863 Reorder the terms: -0.5102040815 + t = 6.689551863 Solving -0.5102040815 + t = 6.689551863 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 = 6.689551863 + 0.5102040815 Combine like terms: -0.5102040815 + 0.5102040815 = 0.0000000000 0.0000000000 + t = 6.689551863 + 0.5102040815 t = 6.689551863 + 0.5102040815 Combine like terms: 6.689551863 + 0.5102040815 = 7.1997559445 t = 7.1997559445 Simplifying t = 7.1997559445Subproblem 2
t + -0.5102040815 = -6.689551863 Simplifying t + -0.5102040815 = -6.689551863 Reorder the terms: -0.5102040815 + t = -6.689551863 Solving -0.5102040815 + t = -6.689551863 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 = -6.689551863 + 0.5102040815 Combine like terms: -0.5102040815 + 0.5102040815 = 0.0000000000 0.0000000000 + t = -6.689551863 + 0.5102040815 t = -6.689551863 + 0.5102040815 Combine like terms: -6.689551863 + 0.5102040815 = -6.1793477815 t = -6.1793477815 Simplifying t = -6.1793477815Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.1997559445, -6.1793477815}
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