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Simplifying -20 = 13.7t + -4.9t2 Solving -20 = 13.7t + -4.9t2 Solving for variable 't'. Reorder the terms: -20 + -13.7t + 4.9t2 = 13.7t + -13.7t + -4.9t2 + 4.9t2 Combine like terms: 13.7t + -13.7t = 0.0 -20 + -13.7t + 4.9t2 = 0.0 + -4.9t2 + 4.9t2 -20 + -13.7t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -20 + -13.7t + 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 + -2.795918367t + t2 = 0 Move the constant term to the right: Add '4.081632653' to each side of the equation. -4.081632653 + -2.795918367t + 4.081632653 + t2 = 0 + 4.081632653 Reorder the terms: -4.081632653 + 4.081632653 + -2.795918367t + t2 = 0 + 4.081632653 Combine like terms: -4.081632653 + 4.081632653 = 0.000000000 0.000000000 + -2.795918367t + t2 = 0 + 4.081632653 -2.795918367t + t2 = 0 + 4.081632653 Combine like terms: 0 + 4.081632653 = 4.081632653 -2.795918367t + t2 = 4.081632653 The t term is -2.795918367t. Take half its coefficient (-1.397959184). Square it (1.954289880) and add it to both sides. Add '1.954289880' to each side of the equation. -2.795918367t + 1.954289880 + t2 = 4.081632653 + 1.954289880 Reorder the terms: 1.954289880 + -2.795918367t + t2 = 4.081632653 + 1.954289880 Combine like terms: 4.081632653 + 1.954289880 = 6.035922533 1.954289880 + -2.795918367t + t2 = 6.035922533 Factor a perfect square on the left side: (t + -1.397959184)(t + -1.397959184) = 6.035922533 Calculate the square root of the right side: 2.456811457 Break this problem into two subproblems by setting (t + -1.397959184) equal to 2.456811457 and -2.456811457.Subproblem 1
t + -1.397959184 = 2.456811457 Simplifying t + -1.397959184 = 2.456811457 Reorder the terms: -1.397959184 + t = 2.456811457 Solving -1.397959184 + t = 2.456811457 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.397959184' to each side of the equation. -1.397959184 + 1.397959184 + t = 2.456811457 + 1.397959184 Combine like terms: -1.397959184 + 1.397959184 = 0.000000000 0.000000000 + t = 2.456811457 + 1.397959184 t = 2.456811457 + 1.397959184 Combine like terms: 2.456811457 + 1.397959184 = 3.854770641 t = 3.854770641 Simplifying t = 3.854770641Subproblem 2
t + -1.397959184 = -2.456811457 Simplifying t + -1.397959184 = -2.456811457 Reorder the terms: -1.397959184 + t = -2.456811457 Solving -1.397959184 + t = -2.456811457 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.397959184' to each side of the equation. -1.397959184 + 1.397959184 + t = -2.456811457 + 1.397959184 Combine like terms: -1.397959184 + 1.397959184 = 0.000000000 0.000000000 + t = -2.456811457 + 1.397959184 t = -2.456811457 + 1.397959184 Combine like terms: -2.456811457 + 1.397959184 = -1.058852273 t = -1.058852273 Simplifying t = -1.058852273Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.854770641, -1.058852273}
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