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Simplifying -4.9t2 + 15t + 2 = 0 Reorder the terms: 2 + 15t + -4.9t2 = 0 Solving 2 + 15t + -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 + -3.06122449t + t2 = 0 Move the constant term to the right: Add '0.4081632653' to each side of the equation. -0.4081632653 + -3.06122449t + 0.4081632653 + t2 = 0 + 0.4081632653 Reorder the terms: -0.4081632653 + 0.4081632653 + -3.06122449t + t2 = 0 + 0.4081632653 Combine like terms: -0.4081632653 + 0.4081632653 = 0.0000000000 0.0000000000 + -3.06122449t + t2 = 0 + 0.4081632653 -3.06122449t + t2 = 0 + 0.4081632653 Combine like terms: 0 + 0.4081632653 = 0.4081632653 -3.06122449t + t2 = 0.4081632653 The t term is -3.06122449t. Take half its coefficient (-1.530612245). Square it (2.342773845) and add it to both sides. Add '2.342773845' to each side of the equation. -3.06122449t + 2.342773845 + t2 = 0.4081632653 + 2.342773845 Reorder the terms: 2.342773845 + -3.06122449t + t2 = 0.4081632653 + 2.342773845 Combine like terms: 0.4081632653 + 2.342773845 = 2.7509371103 2.342773845 + -3.06122449t + t2 = 2.7509371103 Factor a perfect square on the left side: (t + -1.530612245)(t + -1.530612245) = 2.7509371103 Calculate the square root of the right side: 1.65859492 Break this problem into two subproblems by setting (t + -1.530612245) equal to 1.65859492 and -1.65859492.Subproblem 1
t + -1.530612245 = 1.65859492 Simplifying t + -1.530612245 = 1.65859492 Reorder the terms: -1.530612245 + t = 1.65859492 Solving -1.530612245 + t = 1.65859492 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.530612245' to each side of the equation. -1.530612245 + 1.530612245 + t = 1.65859492 + 1.530612245 Combine like terms: -1.530612245 + 1.530612245 = 0.000000000 0.000000000 + t = 1.65859492 + 1.530612245 t = 1.65859492 + 1.530612245 Combine like terms: 1.65859492 + 1.530612245 = 3.189207165 t = 3.189207165 Simplifying t = 3.189207165Subproblem 2
t + -1.530612245 = -1.65859492 Simplifying t + -1.530612245 = -1.65859492 Reorder the terms: -1.530612245 + t = -1.65859492 Solving -1.530612245 + t = -1.65859492 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.530612245' to each side of the equation. -1.530612245 + 1.530612245 + t = -1.65859492 + 1.530612245 Combine like terms: -1.530612245 + 1.530612245 = 0.000000000 0.000000000 + t = -1.65859492 + 1.530612245 t = -1.65859492 + 1.530612245 Combine like terms: -1.65859492 + 1.530612245 = -0.127982675 t = -0.127982675 Simplifying t = -0.127982675Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.189207165, -0.127982675}
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