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Simplifying 16t2 + -230t + -110 = 0 Reorder the terms: -110 + -230t + 16t2 = 0 Solving -110 + -230t + 16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(-55 + -115t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-55 + -115t + 8t2)' equal to zero and attempt to solve: Simplifying -55 + -115t + 8t2 = 0 Solving -55 + -115t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -6.875 + -14.375t + t2 = 0 Move the constant term to the right: Add '6.875' to each side of the equation. -6.875 + -14.375t + 6.875 + t2 = 0 + 6.875 Reorder the terms: -6.875 + 6.875 + -14.375t + t2 = 0 + 6.875 Combine like terms: -6.875 + 6.875 = 0.000 0.000 + -14.375t + t2 = 0 + 6.875 -14.375t + t2 = 0 + 6.875 Combine like terms: 0 + 6.875 = 6.875 -14.375t + t2 = 6.875 The t term is -14.375t. Take half its coefficient (-7.1875). Square it (51.66015625) and add it to both sides. Add '51.66015625' to each side of the equation. -14.375t + 51.66015625 + t2 = 6.875 + 51.66015625 Reorder the terms: 51.66015625 + -14.375t + t2 = 6.875 + 51.66015625 Combine like terms: 6.875 + 51.66015625 = 58.53515625 51.66015625 + -14.375t + t2 = 58.53515625 Factor a perfect square on the left side: (t + -7.1875)(t + -7.1875) = 58.53515625 Calculate the square root of the right side: 7.650827161 Break this problem into two subproblems by setting (t + -7.1875) equal to 7.650827161 and -7.650827161.Subproblem 1
t + -7.1875 = 7.650827161 Simplifying t + -7.1875 = 7.650827161 Reorder the terms: -7.1875 + t = 7.650827161 Solving -7.1875 + t = 7.650827161 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '7.1875' to each side of the equation. -7.1875 + 7.1875 + t = 7.650827161 + 7.1875 Combine like terms: -7.1875 + 7.1875 = 0.0000 0.0000 + t = 7.650827161 + 7.1875 t = 7.650827161 + 7.1875 Combine like terms: 7.650827161 + 7.1875 = 14.838327161 t = 14.838327161 Simplifying t = 14.838327161Subproblem 2
t + -7.1875 = -7.650827161 Simplifying t + -7.1875 = -7.650827161 Reorder the terms: -7.1875 + t = -7.650827161 Solving -7.1875 + t = -7.650827161 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '7.1875' to each side of the equation. -7.1875 + 7.1875 + t = -7.650827161 + 7.1875 Combine like terms: -7.1875 + 7.1875 = 0.0000 0.0000 + t = -7.650827161 + 7.1875 t = -7.650827161 + 7.1875 Combine like terms: -7.650827161 + 7.1875 = -0.463327161 t = -0.463327161 Simplifying t = -0.463327161Solution
The solution to the problem is based on the solutions from the subproblems. t = {14.838327161, -0.463327161}Solution
t = {14.838327161, -0.463327161}
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