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Simplifying 0 = -4.9t2 + 45t + 2 Reorder the terms: 0 = 2 + 45t + -4.9t2 Solving 0 = 2 + 45t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -2 = -2 -2 + -45t + 4.9t2 = 2 + 45t + -4.9t2 + -2 + -45t + 4.9t2 Reorder the terms: -2 + -45t + 4.9t2 = 2 + -2 + 45t + -45t + -4.9t2 + 4.9t2 Combine like terms: 2 + -2 = 0 -2 + -45t + 4.9t2 = 0 + 45t + -45t + -4.9t2 + 4.9t2 -2 + -45t + 4.9t2 = 45t + -45t + -4.9t2 + 4.9t2 Combine like terms: 45t + -45t = 0 -2 + -45t + 4.9t2 = 0 + -4.9t2 + 4.9t2 -2 + -45t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -2 + -45t + 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'. -0.4081632653 + -9.183673469t + t2 = 0 Move the constant term to the right: Add '0.4081632653' to each side of the equation. -0.4081632653 + -9.183673469t + 0.4081632653 + t2 = 0 + 0.4081632653 Reorder the terms: -0.4081632653 + 0.4081632653 + -9.183673469t + t2 = 0 + 0.4081632653 Combine like terms: -0.4081632653 + 0.4081632653 = 0.0000000000 0.0000000000 + -9.183673469t + t2 = 0 + 0.4081632653 -9.183673469t + t2 = 0 + 0.4081632653 Combine like terms: 0 + 0.4081632653 = 0.4081632653 -9.183673469t + t2 = 0.4081632653 The t term is -9.183673469t. Take half its coefficient (-4.591836735). Square it (21.08496460) and add it to both sides. Add '21.08496460' to each side of the equation. -9.183673469t + 21.08496460 + t2 = 0.4081632653 + 21.08496460 Reorder the terms: 21.08496460 + -9.183673469t + t2 = 0.4081632653 + 21.08496460 Combine like terms: 0.4081632653 + 21.08496460 = 21.4931278653 21.08496460 + -9.183673469t + t2 = 21.4931278653 Factor a perfect square on the left side: (t + -4.591836735)(t + -4.591836735) = 21.4931278653 Calculate the square root of the right side: 4.636068147 Break this problem into two subproblems by setting (t + -4.591836735) equal to 4.636068147 and -4.636068147.Subproblem 1
t + -4.591836735 = 4.636068147 Simplifying t + -4.591836735 = 4.636068147 Reorder the terms: -4.591836735 + t = 4.636068147 Solving -4.591836735 + t = 4.636068147 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.591836735' to each side of the equation. -4.591836735 + 4.591836735 + t = 4.636068147 + 4.591836735 Combine like terms: -4.591836735 + 4.591836735 = 0.000000000 0.000000000 + t = 4.636068147 + 4.591836735 t = 4.636068147 + 4.591836735 Combine like terms: 4.636068147 + 4.591836735 = 9.227904882 t = 9.227904882 Simplifying t = 9.227904882Subproblem 2
t + -4.591836735 = -4.636068147 Simplifying t + -4.591836735 = -4.636068147 Reorder the terms: -4.591836735 + t = -4.636068147 Solving -4.591836735 + t = -4.636068147 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.591836735' to each side of the equation. -4.591836735 + 4.591836735 + t = -4.636068147 + 4.591836735 Combine like terms: -4.591836735 + 4.591836735 = 0.000000000 0.000000000 + t = -4.636068147 + 4.591836735 t = -4.636068147 + 4.591836735 Combine like terms: -4.636068147 + 4.591836735 = -0.044231412 t = -0.044231412 Simplifying t = -0.044231412Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.227904882, -0.044231412}
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