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Simplifying 0 = -9.8t2 + 20t + 1.5 Reorder the terms: 0 = 1.5 + 20t + -9.8t2 Solving 0 = 1.5 + 20t + -9.8t2 Solving for variable 't'. Combine like terms: 0 + -1.5 = -1.5 -1.5 + -20t + 9.8t2 = 1.5 + 20t + -9.8t2 + -1.5 + -20t + 9.8t2 Reorder the terms: -1.5 + -20t + 9.8t2 = 1.5 + -1.5 + 20t + -20t + -9.8t2 + 9.8t2 Combine like terms: 1.5 + -1.5 = 0.0 -1.5 + -20t + 9.8t2 = 0.0 + 20t + -20t + -9.8t2 + 9.8t2 -1.5 + -20t + 9.8t2 = 20t + -20t + -9.8t2 + 9.8t2 Combine like terms: 20t + -20t = 0 -1.5 + -20t + 9.8t2 = 0 + -9.8t2 + 9.8t2 -1.5 + -20t + 9.8t2 = -9.8t2 + 9.8t2 Combine like terms: -9.8t2 + 9.8t2 = 0.0 -1.5 + -20t + 9.8t2 = 0.0 Begin completing the square. Divide all terms by 9.8 the coefficient of the squared term: Divide each side by '9.8'. -0.1530612245 + -2.040816327t + t2 = 0 Move the constant term to the right: Add '0.1530612245' to each side of the equation. -0.1530612245 + -2.040816327t + 0.1530612245 + t2 = 0 + 0.1530612245 Reorder the terms: -0.1530612245 + 0.1530612245 + -2.040816327t + t2 = 0 + 0.1530612245 Combine like terms: -0.1530612245 + 0.1530612245 = 0.0000000000 0.0000000000 + -2.040816327t + t2 = 0 + 0.1530612245 -2.040816327t + t2 = 0 + 0.1530612245 Combine like terms: 0 + 0.1530612245 = 0.1530612245 -2.040816327t + t2 = 0.1530612245 The t term is -2.040816327t. Take half its coefficient (-1.020408164). Square it (1.041232821) and add it to both sides. Add '1.041232821' to each side of the equation. -2.040816327t + 1.041232821 + t2 = 0.1530612245 + 1.041232821 Reorder the terms: 1.041232821 + -2.040816327t + t2 = 0.1530612245 + 1.041232821 Combine like terms: 0.1530612245 + 1.041232821 = 1.1942940455 1.041232821 + -2.040816327t + t2 = 1.1942940455 Factor a perfect square on the left side: (t + -1.020408164)(t + -1.020408164) = 1.1942940455 Calculate the square root of the right side: 1.092837612 Break this problem into two subproblems by setting (t + -1.020408164) equal to 1.092837612 and -1.092837612.Subproblem 1
t + -1.020408164 = 1.092837612 Simplifying t + -1.020408164 = 1.092837612 Reorder the terms: -1.020408164 + t = 1.092837612 Solving -1.020408164 + t = 1.092837612 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.020408164' to each side of the equation. -1.020408164 + 1.020408164 + t = 1.092837612 + 1.020408164 Combine like terms: -1.020408164 + 1.020408164 = 0.000000000 0.000000000 + t = 1.092837612 + 1.020408164 t = 1.092837612 + 1.020408164 Combine like terms: 1.092837612 + 1.020408164 = 2.113245776 t = 2.113245776 Simplifying t = 2.113245776Subproblem 2
t + -1.020408164 = -1.092837612 Simplifying t + -1.020408164 = -1.092837612 Reorder the terms: -1.020408164 + t = -1.092837612 Solving -1.020408164 + t = -1.092837612 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.020408164' to each side of the equation. -1.020408164 + 1.020408164 + t = -1.092837612 + 1.020408164 Combine like terms: -1.020408164 + 1.020408164 = 0.000000000 0.000000000 + t = -1.092837612 + 1.020408164 t = -1.092837612 + 1.020408164 Combine like terms: -1.092837612 + 1.020408164 = -0.072429448 t = -0.072429448 Simplifying t = -0.072429448Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.113245776, -0.072429448}
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