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Simplifying 8t2 + 35t + -6 = 0 Reorder the terms: -6 + 35t + 8t2 = 0 Solving -6 + 35t + 8t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.75 + 4.375t + t2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + 4.375t + 0.75 + t2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + 4.375t + t2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + 4.375t + t2 = 0 + 0.75 4.375t + t2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 4.375t + t2 = 0.75 The t term is 4.375t. Take half its coefficient (2.1875). Square it (4.78515625) and add it to both sides. Add '4.78515625' to each side of the equation. 4.375t + 4.78515625 + t2 = 0.75 + 4.78515625 Reorder the terms: 4.78515625 + 4.375t + t2 = 0.75 + 4.78515625 Combine like terms: 0.75 + 4.78515625 = 5.53515625 4.78515625 + 4.375t + t2 = 5.53515625 Factor a perfect square on the left side: (t + 2.1875)(t + 2.1875) = 5.53515625 Calculate the square root of the right side: 2.352691278 Break this problem into two subproblems by setting (t + 2.1875) equal to 2.352691278 and -2.352691278.Subproblem 1
t + 2.1875 = 2.352691278 Simplifying t + 2.1875 = 2.352691278 Reorder the terms: 2.1875 + t = 2.352691278 Solving 2.1875 + t = 2.352691278 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.1875' to each side of the equation. 2.1875 + -2.1875 + t = 2.352691278 + -2.1875 Combine like terms: 2.1875 + -2.1875 = 0.0000 0.0000 + t = 2.352691278 + -2.1875 t = 2.352691278 + -2.1875 Combine like terms: 2.352691278 + -2.1875 = 0.165191278 t = 0.165191278 Simplifying t = 0.165191278Subproblem 2
t + 2.1875 = -2.352691278 Simplifying t + 2.1875 = -2.352691278 Reorder the terms: 2.1875 + t = -2.352691278 Solving 2.1875 + t = -2.352691278 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.1875' to each side of the equation. 2.1875 + -2.1875 + t = -2.352691278 + -2.1875 Combine like terms: 2.1875 + -2.1875 = 0.0000 0.0000 + t = -2.352691278 + -2.1875 t = -2.352691278 + -2.1875 Combine like terms: -2.352691278 + -2.1875 = -4.540191278 t = -4.540191278 Simplifying t = -4.540191278Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.165191278, -4.540191278}
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