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Simplifying 38t + -16t2 + 22 = 0 Reorder the terms: 22 + 38t + -16t2 = 0 Solving 22 + 38t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(11 + 19t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(11 + 19t + -8t2)' equal to zero and attempt to solve: Simplifying 11 + 19t + -8t2 = 0 Solving 11 + 19t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -1.375 + -2.375t + t2 = 0 Move the constant term to the right: Add '1.375' to each side of the equation. -1.375 + -2.375t + 1.375 + t2 = 0 + 1.375 Reorder the terms: -1.375 + 1.375 + -2.375t + t2 = 0 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + -2.375t + t2 = 0 + 1.375 -2.375t + t2 = 0 + 1.375 Combine like terms: 0 + 1.375 = 1.375 -2.375t + t2 = 1.375 The t term is -2.375t. Take half its coefficient (-1.1875). Square it (1.41015625) and add it to both sides. Add '1.41015625' to each side of the equation. -2.375t + 1.41015625 + t2 = 1.375 + 1.41015625 Reorder the terms: 1.41015625 + -2.375t + t2 = 1.375 + 1.41015625 Combine like terms: 1.375 + 1.41015625 = 2.78515625 1.41015625 + -2.375t + t2 = 2.78515625 Factor a perfect square on the left side: (t + -1.1875)(t + -1.1875) = 2.78515625 Calculate the square root of the right side: 1.66887874 Break this problem into two subproblems by setting (t + -1.1875) equal to 1.66887874 and -1.66887874.Subproblem 1
t + -1.1875 = 1.66887874 Simplifying t + -1.1875 = 1.66887874 Reorder the terms: -1.1875 + t = 1.66887874 Solving -1.1875 + t = 1.66887874 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.1875' to each side of the equation. -1.1875 + 1.1875 + t = 1.66887874 + 1.1875 Combine like terms: -1.1875 + 1.1875 = 0.0000 0.0000 + t = 1.66887874 + 1.1875 t = 1.66887874 + 1.1875 Combine like terms: 1.66887874 + 1.1875 = 2.85637874 t = 2.85637874 Simplifying t = 2.85637874Subproblem 2
t + -1.1875 = -1.66887874 Simplifying t + -1.1875 = -1.66887874 Reorder the terms: -1.1875 + t = -1.66887874 Solving -1.1875 + t = -1.66887874 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.1875' to each side of the equation. -1.1875 + 1.1875 + t = -1.66887874 + 1.1875 Combine like terms: -1.1875 + 1.1875 = 0.0000 0.0000 + t = -1.66887874 + 1.1875 t = -1.66887874 + 1.1875 Combine like terms: -1.66887874 + 1.1875 = -0.48137874 t = -0.48137874 Simplifying t = -0.48137874Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.85637874, -0.48137874}Solution
t = {2.85637874, -0.48137874}
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