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Simplifying 20 = -4.9t2 + 40t Reorder the terms: 20 = 40t + -4.9t2 Solving 20 = 40t + -4.9t2 Solving for variable 't'. Reorder the terms: 20 + -40t + 4.9t2 = 40t + -40t + -4.9t2 + 4.9t2 Combine like terms: 40t + -40t = 0 20 + -40t + 4.9t2 = 0 + -4.9t2 + 4.9t2 20 + -40t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 20 + -40t + 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'. 4.081632653 + -8.163265306t + t2 = 0 Move the constant term to the right: Add '-4.081632653' to each side of the equation. 4.081632653 + -8.163265306t + -4.081632653 + t2 = 0 + -4.081632653 Reorder the terms: 4.081632653 + -4.081632653 + -8.163265306t + t2 = 0 + -4.081632653 Combine like terms: 4.081632653 + -4.081632653 = 0.000000000 0.000000000 + -8.163265306t + t2 = 0 + -4.081632653 -8.163265306t + t2 = 0 + -4.081632653 Combine like terms: 0 + -4.081632653 = -4.081632653 -8.163265306t + t2 = -4.081632653 The t term is -8.163265306t. Take half its coefficient (-4.081632653). Square it (16.65972511) and add it to both sides. Add '16.65972511' to each side of the equation. -8.163265306t + 16.65972511 + t2 = -4.081632653 + 16.65972511 Reorder the terms: 16.65972511 + -8.163265306t + t2 = -4.081632653 + 16.65972511 Combine like terms: -4.081632653 + 16.65972511 = 12.578092457 16.65972511 + -8.163265306t + t2 = 12.578092457 Factor a perfect square on the left side: (t + -4.081632653)(t + -4.081632653) = 12.578092457 Calculate the square root of the right side: 3.546560652 Break this problem into two subproblems by setting (t + -4.081632653) equal to 3.546560652 and -3.546560652.Subproblem 1
t + -4.081632653 = 3.546560652 Simplifying t + -4.081632653 = 3.546560652 Reorder the terms: -4.081632653 + t = 3.546560652 Solving -4.081632653 + t = 3.546560652 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.081632653' to each side of the equation. -4.081632653 + 4.081632653 + t = 3.546560652 + 4.081632653 Combine like terms: -4.081632653 + 4.081632653 = 0.000000000 0.000000000 + t = 3.546560652 + 4.081632653 t = 3.546560652 + 4.081632653 Combine like terms: 3.546560652 + 4.081632653 = 7.628193305 t = 7.628193305 Simplifying t = 7.628193305Subproblem 2
t + -4.081632653 = -3.546560652 Simplifying t + -4.081632653 = -3.546560652 Reorder the terms: -4.081632653 + t = -3.546560652 Solving -4.081632653 + t = -3.546560652 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.081632653' to each side of the equation. -4.081632653 + 4.081632653 + t = -3.546560652 + 4.081632653 Combine like terms: -4.081632653 + 4.081632653 = 0.000000000 0.000000000 + t = -3.546560652 + 4.081632653 t = -3.546560652 + 4.081632653 Combine like terms: -3.546560652 + 4.081632653 = 0.535072001 t = 0.535072001 Simplifying t = 0.535072001Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.628193305, 0.535072001}
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