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Simplifying 4.9 * 340t2 + t + -6.1 = 0 Multiply 4.9 * 340 1666t2 + t + -6.1 = 0 Reorder the terms: -6.1 + t + 1666t2 = 0 Solving -6.1 + t + 1666t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 1666 the coefficient of the squared term: Divide each side by '1666'. -0.003661464586 + 0.0006002400960t + t2 = 0 Move the constant term to the right: Add '0.003661464586' to each side of the equation. -0.003661464586 + 0.0006002400960t + 0.003661464586 + t2 = 0 + 0.003661464586 Reorder the terms: -0.003661464586 + 0.003661464586 + 0.0006002400960t + t2 = 0 + 0.003661464586 Combine like terms: -0.003661464586 + 0.003661464586 = 0.000000000000 0.000000000000 + 0.0006002400960t + t2 = 0 + 0.003661464586 0.0006002400960t + t2 = 0 + 0.003661464586 Combine like terms: 0 + 0.003661464586 = 0.003661464586 0.0006002400960t + t2 = 0.003661464586 The t term is t. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.0006002400960t + 0.25 + t2 = 0.003661464586 + 0.25 Reorder the terms: 0.25 + 0.0006002400960t + t2 = 0.003661464586 + 0.25 Combine like terms: 0.003661464586 + 0.25 = 0.253661464586 0.25 + 0.0006002400960t + t2 = 0.253661464586 Factor a perfect square on the left side: (t + 0.5)(t + 0.5) = 0.253661464586 Calculate the square root of the right side: 0.503648156 Break this problem into two subproblems by setting (t + 0.5) equal to 0.503648156 and -0.503648156.Subproblem 1
t + 0.5 = 0.503648156 Simplifying t + 0.5 = 0.503648156 Reorder the terms: 0.5 + t = 0.503648156 Solving 0.5 + t = 0.503648156 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = 0.503648156 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = 0.503648156 + -0.5 t = 0.503648156 + -0.5 Combine like terms: 0.503648156 + -0.5 = 0.003648156 t = 0.003648156 Simplifying t = 0.003648156Subproblem 2
t + 0.5 = -0.503648156 Simplifying t + 0.5 = -0.503648156 Reorder the terms: 0.5 + t = -0.503648156 Solving 0.5 + t = -0.503648156 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = -0.503648156 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = -0.503648156 + -0.5 t = -0.503648156 + -0.5 Combine like terms: -0.503648156 + -0.5 = -1.003648156 t = -1.003648156 Simplifying t = -1.003648156Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.003648156, -1.003648156}
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