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Simplifying -4.9t2 + 5.8t + 6 = 0 Reorder the terms: 6 + 5.8t + -4.9t2 = 0 Solving 6 + 5.8t + -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'. -1.224489796 + -1.183673469t + t2 = 0 Move the constant term to the right: Add '1.224489796' to each side of the equation. -1.224489796 + -1.183673469t + 1.224489796 + t2 = 0 + 1.224489796 Reorder the terms: -1.224489796 + 1.224489796 + -1.183673469t + t2 = 0 + 1.224489796 Combine like terms: -1.224489796 + 1.224489796 = 0.000000000 0.000000000 + -1.183673469t + t2 = 0 + 1.224489796 -1.183673469t + t2 = 0 + 1.224489796 Combine like terms: 0 + 1.224489796 = 1.224489796 -1.183673469t + t2 = 1.224489796 The t term is -1.183673469t. Take half its coefficient (-0.5918367345). Square it (0.3502707203) and add it to both sides. Add '0.3502707203' to each side of the equation. -1.183673469t + 0.3502707203 + t2 = 1.224489796 + 0.3502707203 Reorder the terms: 0.3502707203 + -1.183673469t + t2 = 1.224489796 + 0.3502707203 Combine like terms: 1.224489796 + 0.3502707203 = 1.5747605163 0.3502707203 + -1.183673469t + t2 = 1.5747605163 Factor a perfect square on the left side: (t + -0.5918367345)(t + -0.5918367345) = 1.5747605163 Calculate the square root of the right side: 1.254894624 Break this problem into two subproblems by setting (t + -0.5918367345) equal to 1.254894624 and -1.254894624.Subproblem 1
t + -0.5918367345 = 1.254894624 Simplifying t + -0.5918367345 = 1.254894624 Reorder the terms: -0.5918367345 + t = 1.254894624 Solving -0.5918367345 + t = 1.254894624 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5918367345' to each side of the equation. -0.5918367345 + 0.5918367345 + t = 1.254894624 + 0.5918367345 Combine like terms: -0.5918367345 + 0.5918367345 = 0.0000000000 0.0000000000 + t = 1.254894624 + 0.5918367345 t = 1.254894624 + 0.5918367345 Combine like terms: 1.254894624 + 0.5918367345 = 1.8467313585 t = 1.8467313585 Simplifying t = 1.8467313585Subproblem 2
t + -0.5918367345 = -1.254894624 Simplifying t + -0.5918367345 = -1.254894624 Reorder the terms: -0.5918367345 + t = -1.254894624 Solving -0.5918367345 + t = -1.254894624 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5918367345' to each side of the equation. -0.5918367345 + 0.5918367345 + t = -1.254894624 + 0.5918367345 Combine like terms: -0.5918367345 + 0.5918367345 = 0.0000000000 0.0000000000 + t = -1.254894624 + 0.5918367345 t = -1.254894624 + 0.5918367345 Combine like terms: -1.254894624 + 0.5918367345 = -0.6630578895 t = -0.6630578895 Simplifying t = -0.6630578895Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.8467313585, -0.6630578895}
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