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Simplifying 100 = 15(t) + 4.9t2 Solving 100 = 15t + 4.9t2 Solving for variable 't'. Reorder the terms: 100 + -15t + -4.9t2 = 15t + -15t + 4.9t2 + -4.9t2 Combine like terms: 15t + -15t = 0 100 + -15t + -4.9t2 = 0 + 4.9t2 + -4.9t2 100 + -15t + -4.9t2 = 4.9t2 + -4.9t2 Combine like terms: 4.9t2 + -4.9t2 = 0.0 100 + -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'. -20.40816327 + 3.06122449t + t2 = 0 Move the constant term to the right: Add '20.40816327' to each side of the equation. -20.40816327 + 3.06122449t + 20.40816327 + t2 = 0 + 20.40816327 Reorder the terms: -20.40816327 + 20.40816327 + 3.06122449t + t2 = 0 + 20.40816327 Combine like terms: -20.40816327 + 20.40816327 = 0.00000000 0.00000000 + 3.06122449t + t2 = 0 + 20.40816327 3.06122449t + t2 = 0 + 20.40816327 Combine like terms: 0 + 20.40816327 = 20.40816327 3.06122449t + t2 = 20.40816327 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 = 20.40816327 + 2.342773845 Reorder the terms: 2.342773845 + 3.06122449t + t2 = 20.40816327 + 2.342773845 Combine like terms: 20.40816327 + 2.342773845 = 22.750937115 2.342773845 + 3.06122449t + t2 = 22.750937115 Factor a perfect square on the left side: (t + 1.530612245)(t + 1.530612245) = 22.750937115 Calculate the square root of the right side: 4.769794242 Break this problem into two subproblems by setting (t + 1.530612245) equal to 4.769794242 and -4.769794242.Subproblem 1
t + 1.530612245 = 4.769794242 Simplifying t + 1.530612245 = 4.769794242 Reorder the terms: 1.530612245 + t = 4.769794242 Solving 1.530612245 + t = 4.769794242 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 = 4.769794242 + -1.530612245 Combine like terms: 1.530612245 + -1.530612245 = 0.000000000 0.000000000 + t = 4.769794242 + -1.530612245 t = 4.769794242 + -1.530612245 Combine like terms: 4.769794242 + -1.530612245 = 3.239181997 t = 3.239181997 Simplifying t = 3.239181997Subproblem 2
t + 1.530612245 = -4.769794242 Simplifying t + 1.530612245 = -4.769794242 Reorder the terms: 1.530612245 + t = -4.769794242 Solving 1.530612245 + t = -4.769794242 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 = -4.769794242 + -1.530612245 Combine like terms: 1.530612245 + -1.530612245 = 0.000000000 0.000000000 + t = -4.769794242 + -1.530612245 t = -4.769794242 + -1.530612245 Combine like terms: -4.769794242 + -1.530612245 = -6.300406487 t = -6.300406487 Simplifying t = -6.300406487Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.239181997, -6.300406487}
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