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Simplifying 16.1t2 + 13.8996t + -3 = 0 Reorder the terms: -3 + 13.8996t + 16.1t2 = 0 Solving -3 + 13.8996t + 16.1t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 16.1 the coefficient of the squared term: Divide each side by '16.1'. -0.1863354037 + 0.8633291925t + t2 = 0 Move the constant term to the right: Add '0.1863354037' to each side of the equation. -0.1863354037 + 0.8633291925t + 0.1863354037 + t2 = 0 + 0.1863354037 Reorder the terms: -0.1863354037 + 0.1863354037 + 0.8633291925t + t2 = 0 + 0.1863354037 Combine like terms: -0.1863354037 + 0.1863354037 = 0.0000000000 0.0000000000 + 0.8633291925t + t2 = 0 + 0.1863354037 0.8633291925t + t2 = 0 + 0.1863354037 Combine like terms: 0 + 0.1863354037 = 0.1863354037 0.8633291925t + t2 = 0.1863354037 The t term is 0.8633291925t. Take half its coefficient (0.4316645963). Square it (0.1863343237) and add it to both sides. Add '0.1863343237' to each side of the equation. 0.8633291925t + 0.1863343237 + t2 = 0.1863354037 + 0.1863343237 Reorder the terms: 0.1863343237 + 0.8633291925t + t2 = 0.1863354037 + 0.1863343237 Combine like terms: 0.1863354037 + 0.1863343237 = 0.3726697274 0.1863343237 + 0.8633291925t + t2 = 0.3726697274 Factor a perfect square on the left side: (t + 0.4316645963)(t + 0.4316645963) = 0.3726697274 Calculate the square root of the right side: 0.610466811 Break this problem into two subproblems by setting (t + 0.4316645963) equal to 0.610466811 and -0.610466811.Subproblem 1
t + 0.4316645963 = 0.610466811 Simplifying t + 0.4316645963 = 0.610466811 Reorder the terms: 0.4316645963 + t = 0.610466811 Solving 0.4316645963 + t = 0.610466811 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.4316645963' to each side of the equation. 0.4316645963 + -0.4316645963 + t = 0.610466811 + -0.4316645963 Combine like terms: 0.4316645963 + -0.4316645963 = 0.0000000000 0.0000000000 + t = 0.610466811 + -0.4316645963 t = 0.610466811 + -0.4316645963 Combine like terms: 0.610466811 + -0.4316645963 = 0.1788022147 t = 0.1788022147 Simplifying t = 0.1788022147Subproblem 2
t + 0.4316645963 = -0.610466811 Simplifying t + 0.4316645963 = -0.610466811 Reorder the terms: 0.4316645963 + t = -0.610466811 Solving 0.4316645963 + t = -0.610466811 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.4316645963' to each side of the equation. 0.4316645963 + -0.4316645963 + t = -0.610466811 + -0.4316645963 Combine like terms: 0.4316645963 + -0.4316645963 = 0.0000000000 0.0000000000 + t = -0.610466811 + -0.4316645963 t = -0.610466811 + -0.4316645963 Combine like terms: -0.610466811 + -0.4316645963 = -1.0421314073 t = -1.0421314073 Simplifying t = -1.0421314073Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.1788022147, -1.0421314073}
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