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Simplifying 0 = -4.9t2 + 15t + 0.4 Reorder the terms: 0 = 0.4 + 15t + -4.9t2 Solving 0 = 0.4 + 15t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -0.4 = -0.4 -0.4 + -15t + 4.9t2 = 0.4 + 15t + -4.9t2 + -0.4 + -15t + 4.9t2 Reorder the terms: -0.4 + -15t + 4.9t2 = 0.4 + -0.4 + 15t + -15t + -4.9t2 + 4.9t2 Combine like terms: 0.4 + -0.4 = 0.0 -0.4 + -15t + 4.9t2 = 0.0 + 15t + -15t + -4.9t2 + 4.9t2 -0.4 + -15t + 4.9t2 = 15t + -15t + -4.9t2 + 4.9t2 Combine like terms: 15t + -15t = 0 -0.4 + -15t + 4.9t2 = 0 + -4.9t2 + 4.9t2 -0.4 + -15t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -0.4 + -15t + 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'. -0.08163265306 + -3.06122449t + t2 = 0 Move the constant term to the right: Add '0.08163265306' to each side of the equation. -0.08163265306 + -3.06122449t + 0.08163265306 + t2 = 0 + 0.08163265306 Reorder the terms: -0.08163265306 + 0.08163265306 + -3.06122449t + t2 = 0 + 0.08163265306 Combine like terms: -0.08163265306 + 0.08163265306 = 0.00000000000 0.00000000000 + -3.06122449t + t2 = 0 + 0.08163265306 -3.06122449t + t2 = 0 + 0.08163265306 Combine like terms: 0 + 0.08163265306 = 0.08163265306 -3.06122449t + t2 = 0.08163265306 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 = 0.08163265306 + 2.342773845 Reorder the terms: 2.342773845 + -3.06122449t + t2 = 0.08163265306 + 2.342773845 Combine like terms: 0.08163265306 + 2.342773845 = 2.42440649806 2.342773845 + -3.06122449t + t2 = 2.42440649806 Factor a perfect square on the left side: (t + -1.530612245)(t + -1.530612245) = 2.42440649806 Calculate the square root of the right side: 1.557050577 Break this problem into two subproblems by setting (t + -1.530612245) equal to 1.557050577 and -1.557050577.Subproblem 1
t + -1.530612245 = 1.557050577 Simplifying t + -1.530612245 = 1.557050577 Reorder the terms: -1.530612245 + t = 1.557050577 Solving -1.530612245 + t = 1.557050577 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 = 1.557050577 + 1.530612245 Combine like terms: -1.530612245 + 1.530612245 = 0.000000000 0.000000000 + t = 1.557050577 + 1.530612245 t = 1.557050577 + 1.530612245 Combine like terms: 1.557050577 + 1.530612245 = 3.087662822 t = 3.087662822 Simplifying t = 3.087662822Subproblem 2
t + -1.530612245 = -1.557050577 Simplifying t + -1.530612245 = -1.557050577 Reorder the terms: -1.530612245 + t = -1.557050577 Solving -1.530612245 + t = -1.557050577 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 = -1.557050577 + 1.530612245 Combine like terms: -1.530612245 + 1.530612245 = 0.000000000 0.000000000 + t = -1.557050577 + 1.530612245 t = -1.557050577 + 1.530612245 Combine like terms: -1.557050577 + 1.530612245 = -0.026438332 t = -0.026438332 Simplifying t = -0.026438332Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.087662822, -0.026438332}
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