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Simplifying 0.0001185t2 + -0.0122t + 0.0514 = 0 Reorder the terms: 0.0514 + -0.0122t + 0.0001185t2 = 0 Solving 0.0514 + -0.0122t + 0.0001185t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 0.0001185 the coefficient of the squared term: Divide each side by '0.0001185'. 433.7552743 + -102.9535865t + t2 = 0 Move the constant term to the right: Add '-433.7552743' to each side of the equation. 433.7552743 + -102.9535865t + -433.7552743 + t2 = 0 + -433.7552743 Reorder the terms: 433.7552743 + -433.7552743 + -102.9535865t + t2 = 0 + -433.7552743 Combine like terms: 433.7552743 + -433.7552743 = 0.0000000 0.0000000 + -102.9535865t + t2 = 0 + -433.7552743 -102.9535865t + t2 = 0 + -433.7552743 Combine like terms: 0 + -433.7552743 = -433.7552743 -102.9535865t + t2 = -433.7552743 The t term is -102.9535865t. Take half its coefficient (-51.47679325). Square it (2649.860243) and add it to both sides. Add '2649.860243' to each side of the equation. -102.9535865t + 2649.860243 + t2 = -433.7552743 + 2649.860243 Reorder the terms: 2649.860243 + -102.9535865t + t2 = -433.7552743 + 2649.860243 Combine like terms: -433.7552743 + 2649.860243 = 2216.1049687 2649.860243 + -102.9535865t + t2 = 2216.1049687 Factor a perfect square on the left side: (t + -51.47679325)(t + -51.47679325) = 2216.1049687 Calculate the square root of the right side: 47.075524094 Break this problem into two subproblems by setting (t + -51.47679325) equal to 47.075524094 and -47.075524094.Subproblem 1
t + -51.47679325 = 47.075524094 Simplifying t + -51.47679325 = 47.075524094 Reorder the terms: -51.47679325 + t = 47.075524094 Solving -51.47679325 + t = 47.075524094 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '51.47679325' to each side of the equation. -51.47679325 + 51.47679325 + t = 47.075524094 + 51.47679325 Combine like terms: -51.47679325 + 51.47679325 = 0.00000000 0.00000000 + t = 47.075524094 + 51.47679325 t = 47.075524094 + 51.47679325 Combine like terms: 47.075524094 + 51.47679325 = 98.552317344 t = 98.552317344 Simplifying t = 98.552317344Subproblem 2
t + -51.47679325 = -47.075524094 Simplifying t + -51.47679325 = -47.075524094 Reorder the terms: -51.47679325 + t = -47.075524094 Solving -51.47679325 + t = -47.075524094 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '51.47679325' to each side of the equation. -51.47679325 + 51.47679325 + t = -47.075524094 + 51.47679325 Combine like terms: -51.47679325 + 51.47679325 = 0.00000000 0.00000000 + t = -47.075524094 + 51.47679325 t = -47.075524094 + 51.47679325 Combine like terms: -47.075524094 + 51.47679325 = 4.401269156 t = 4.401269156 Simplifying t = 4.401269156Solution
The solution to the problem is based on the solutions from the subproblems. t = {98.552317344, 4.401269156}
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