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Simplifying -4.9t2 + 21t + 2 = 0 Reorder the terms: 2 + 21t + -4.9t2 = 0 Solving 2 + 21t + -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'. -0.4081632653 + -4.285714286t + t2 = 0 Move the constant term to the right: Add '0.4081632653' to each side of the equation. -0.4081632653 + -4.285714286t + 0.4081632653 + t2 = 0 + 0.4081632653 Reorder the terms: -0.4081632653 + 0.4081632653 + -4.285714286t + t2 = 0 + 0.4081632653 Combine like terms: -0.4081632653 + 0.4081632653 = 0.0000000000 0.0000000000 + -4.285714286t + t2 = 0 + 0.4081632653 -4.285714286t + t2 = 0 + 0.4081632653 Combine like terms: 0 + 0.4081632653 = 0.4081632653 -4.285714286t + t2 = 0.4081632653 The t term is -4.285714286t. Take half its coefficient (-2.142857143). Square it (4.591836735) and add it to both sides. Add '4.591836735' to each side of the equation. -4.285714286t + 4.591836735 + t2 = 0.4081632653 + 4.591836735 Reorder the terms: 4.591836735 + -4.285714286t + t2 = 0.4081632653 + 4.591836735 Combine like terms: 0.4081632653 + 4.591836735 = 5.0000000003 4.591836735 + -4.285714286t + t2 = 5.0000000003 Factor a perfect square on the left side: (t + -2.142857143)(t + -2.142857143) = 5.0000000003 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (t + -2.142857143) equal to 2.236067978 and -2.236067978.Subproblem 1
t + -2.142857143 = 2.236067978 Simplifying t + -2.142857143 = 2.236067978 Reorder the terms: -2.142857143 + t = 2.236067978 Solving -2.142857143 + t = 2.236067978 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.142857143' to each side of the equation. -2.142857143 + 2.142857143 + t = 2.236067978 + 2.142857143 Combine like terms: -2.142857143 + 2.142857143 = 0.000000000 0.000000000 + t = 2.236067978 + 2.142857143 t = 2.236067978 + 2.142857143 Combine like terms: 2.236067978 + 2.142857143 = 4.378925121 t = 4.378925121 Simplifying t = 4.378925121Subproblem 2
t + -2.142857143 = -2.236067978 Simplifying t + -2.142857143 = -2.236067978 Reorder the terms: -2.142857143 + t = -2.236067978 Solving -2.142857143 + t = -2.236067978 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.142857143' to each side of the equation. -2.142857143 + 2.142857143 + t = -2.236067978 + 2.142857143 Combine like terms: -2.142857143 + 2.142857143 = 0.000000000 0.000000000 + t = -2.236067978 + 2.142857143 t = -2.236067978 + 2.142857143 Combine like terms: -2.236067978 + 2.142857143 = -0.093210835 t = -0.093210835 Simplifying t = -0.093210835Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.378925121, -0.093210835}
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