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Simplifying -10.5t2 + 66.3t + 6 = 0 Reorder the terms: 6 + 66.3t + -10.5t2 = 0 Solving 6 + 66.3t + -10.5t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -10.5 the coefficient of the squared term: Divide each side by '-10.5'. -0.5714285714 + -6.314285714t + t2 = 0 Move the constant term to the right: Add '0.5714285714' to each side of the equation. -0.5714285714 + -6.314285714t + 0.5714285714 + t2 = 0 + 0.5714285714 Reorder the terms: -0.5714285714 + 0.5714285714 + -6.314285714t + t2 = 0 + 0.5714285714 Combine like terms: -0.5714285714 + 0.5714285714 = 0.0000000000 0.0000000000 + -6.314285714t + t2 = 0 + 0.5714285714 -6.314285714t + t2 = 0 + 0.5714285714 Combine like terms: 0 + 0.5714285714 = 0.5714285714 -6.314285714t + t2 = 0.5714285714 The t term is -6.314285714t. Take half its coefficient (-3.157142857). Square it (9.967551020) and add it to both sides. Add '9.967551020' to each side of the equation. -6.314285714t + 9.967551020 + t2 = 0.5714285714 + 9.967551020 Reorder the terms: 9.967551020 + -6.314285714t + t2 = 0.5714285714 + 9.967551020 Combine like terms: 0.5714285714 + 9.967551020 = 10.5389795914 9.967551020 + -6.314285714t + t2 = 10.5389795914 Factor a perfect square on the left side: (t + -3.157142857)(t + -3.157142857) = 10.5389795914 Calculate the square root of the right side: 3.246379459 Break this problem into two subproblems by setting (t + -3.157142857) equal to 3.246379459 and -3.246379459.Subproblem 1
t + -3.157142857 = 3.246379459 Simplifying t + -3.157142857 = 3.246379459 Reorder the terms: -3.157142857 + t = 3.246379459 Solving -3.157142857 + t = 3.246379459 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.157142857' to each side of the equation. -3.157142857 + 3.157142857 + t = 3.246379459 + 3.157142857 Combine like terms: -3.157142857 + 3.157142857 = 0.000000000 0.000000000 + t = 3.246379459 + 3.157142857 t = 3.246379459 + 3.157142857 Combine like terms: 3.246379459 + 3.157142857 = 6.403522316 t = 6.403522316 Simplifying t = 6.403522316Subproblem 2
t + -3.157142857 = -3.246379459 Simplifying t + -3.157142857 = -3.246379459 Reorder the terms: -3.157142857 + t = -3.246379459 Solving -3.157142857 + t = -3.246379459 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.157142857' to each side of the equation. -3.157142857 + 3.157142857 + t = -3.246379459 + 3.157142857 Combine like terms: -3.157142857 + 3.157142857 = 0.000000000 0.000000000 + t = -3.246379459 + 3.157142857 t = -3.246379459 + 3.157142857 Combine like terms: -3.246379459 + 3.157142857 = -0.089236602 t = -0.089236602 Simplifying t = -0.089236602Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.403522316, -0.089236602}
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