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Simplifying 0.5t = 0.8 + -4.9t2 Solving 0.5t = 0.8 + -4.9t2 Solving for variable 't'. Reorder the terms: -0.8 + 0.5t + 4.9t2 = 0.8 + -4.9t2 + -0.8 + 4.9t2 Reorder the terms: -0.8 + 0.5t + 4.9t2 = 0.8 + -0.8 + -4.9t2 + 4.9t2 Combine like terms: 0.8 + -0.8 = 0.0 -0.8 + 0.5t + 4.9t2 = 0.0 + -4.9t2 + 4.9t2 -0.8 + 0.5t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -0.8 + 0.5t + 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'. -0.1632653061 + 0.1020408163t + t2 = 0 Move the constant term to the right: Add '0.1632653061' to each side of the equation. -0.1632653061 + 0.1020408163t + 0.1632653061 + t2 = 0 + 0.1632653061 Reorder the terms: -0.1632653061 + 0.1632653061 + 0.1020408163t + t2 = 0 + 0.1632653061 Combine like terms: -0.1632653061 + 0.1632653061 = 0.0000000000 0.0000000000 + 0.1020408163t + t2 = 0 + 0.1632653061 0.1020408163t + t2 = 0 + 0.1632653061 Combine like terms: 0 + 0.1632653061 = 0.1632653061 0.1020408163t + t2 = 0.1632653061 The t term is 0.1020408163t. Take half its coefficient (0.05102040815). Square it (0.002603082048) and add it to both sides. Add '0.002603082048' to each side of the equation. 0.1020408163t + 0.002603082048 + t2 = 0.1632653061 + 0.002603082048 Reorder the terms: 0.002603082048 + 0.1020408163t + t2 = 0.1632653061 + 0.002603082048 Combine like terms: 0.1632653061 + 0.002603082048 = 0.165868388148 0.002603082048 + 0.1020408163t + t2 = 0.165868388148 Factor a perfect square on the left side: (t + 0.05102040815)(t + 0.05102040815) = 0.165868388148 Calculate the square root of the right side: 0.407269429 Break this problem into two subproblems by setting (t + 0.05102040815) equal to 0.407269429 and -0.407269429.Subproblem 1
t + 0.05102040815 = 0.407269429 Simplifying t + 0.05102040815 = 0.407269429 Reorder the terms: 0.05102040815 + t = 0.407269429 Solving 0.05102040815 + t = 0.407269429 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.05102040815' to each side of the equation. 0.05102040815 + -0.05102040815 + t = 0.407269429 + -0.05102040815 Combine like terms: 0.05102040815 + -0.05102040815 = 0.00000000000 0.00000000000 + t = 0.407269429 + -0.05102040815 t = 0.407269429 + -0.05102040815 Combine like terms: 0.407269429 + -0.05102040815 = 0.35624902085 t = 0.35624902085 Simplifying t = 0.35624902085Subproblem 2
t + 0.05102040815 = -0.407269429 Simplifying t + 0.05102040815 = -0.407269429 Reorder the terms: 0.05102040815 + t = -0.407269429 Solving 0.05102040815 + t = -0.407269429 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.05102040815' to each side of the equation. 0.05102040815 + -0.05102040815 + t = -0.407269429 + -0.05102040815 Combine like terms: 0.05102040815 + -0.05102040815 = 0.00000000000 0.00000000000 + t = -0.407269429 + -0.05102040815 t = -0.407269429 + -0.05102040815 Combine like terms: -0.407269429 + -0.05102040815 = -0.45828983715 t = -0.45828983715 Simplifying t = -0.45828983715Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.35624902085, -0.45828983715}
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