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Simplifying 4.9t2 + 17.9t + 5 = 0 Reorder the terms: 5 + 17.9t + 4.9t2 = 0 Solving 5 + 17.9t + 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'. 1.020408163 + 3.653061224t + t2 = 0 Move the constant term to the right: Add '-1.020408163' to each side of the equation. 1.020408163 + 3.653061224t + -1.020408163 + t2 = 0 + -1.020408163 Reorder the terms: 1.020408163 + -1.020408163 + 3.653061224t + t2 = 0 + -1.020408163 Combine like terms: 1.020408163 + -1.020408163 = 0.000000000 0.000000000 + 3.653061224t + t2 = 0 + -1.020408163 3.653061224t + t2 = 0 + -1.020408163 Combine like terms: 0 + -1.020408163 = -1.020408163 3.653061224t + t2 = -1.020408163 The t term is 3.653061224t. Take half its coefficient (1.826530612). Square it (3.336214077) and add it to both sides. Add '3.336214077' to each side of the equation. 3.653061224t + 3.336214077 + t2 = -1.020408163 + 3.336214077 Reorder the terms: 3.336214077 + 3.653061224t + t2 = -1.020408163 + 3.336214077 Combine like terms: -1.020408163 + 3.336214077 = 2.315805914 3.336214077 + 3.653061224t + t2 = 2.315805914 Factor a perfect square on the left side: (t + 1.826530612)(t + 1.826530612) = 2.315805914 Calculate the square root of the right side: 1.521777222 Break this problem into two subproblems by setting (t + 1.826530612) equal to 1.521777222 and -1.521777222.Subproblem 1
t + 1.826530612 = 1.521777222 Simplifying t + 1.826530612 = 1.521777222 Reorder the terms: 1.826530612 + t = 1.521777222 Solving 1.826530612 + t = 1.521777222 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.826530612' to each side of the equation. 1.826530612 + -1.826530612 + t = 1.521777222 + -1.826530612 Combine like terms: 1.826530612 + -1.826530612 = 0.000000000 0.000000000 + t = 1.521777222 + -1.826530612 t = 1.521777222 + -1.826530612 Combine like terms: 1.521777222 + -1.826530612 = -0.30475339 t = -0.30475339 Simplifying t = -0.30475339Subproblem 2
t + 1.826530612 = -1.521777222 Simplifying t + 1.826530612 = -1.521777222 Reorder the terms: 1.826530612 + t = -1.521777222 Solving 1.826530612 + t = -1.521777222 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.826530612' to each side of the equation. 1.826530612 + -1.826530612 + t = -1.521777222 + -1.826530612 Combine like terms: 1.826530612 + -1.826530612 = 0.000000000 0.000000000 + t = -1.521777222 + -1.826530612 t = -1.521777222 + -1.826530612 Combine like terms: -1.521777222 + -1.826530612 = -3.348307834 t = -3.348307834 Simplifying t = -3.348307834Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.30475339, -3.348307834}
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