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Simplifying 11t2 + 2t + -44 = 0 Reorder the terms: -44 + 2t + 11t2 = 0 Solving -44 + 2t + 11t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -4 + 0.1818181818t + t2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 0.1818181818t + 4 + t2 = 0 + 4 Reorder the terms: -4 + 4 + 0.1818181818t + t2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 0.1818181818t + t2 = 0 + 4 0.1818181818t + t2 = 0 + 4 Combine like terms: 0 + 4 = 4 0.1818181818t + t2 = 4 The t term is 0.1818181818t. Take half its coefficient (0.0909090909). Square it (0.008264462808) and add it to both sides. Add '0.008264462808' to each side of the equation. 0.1818181818t + 0.008264462808 + t2 = 4 + 0.008264462808 Reorder the terms: 0.008264462808 + 0.1818181818t + t2 = 4 + 0.008264462808 Combine like terms: 4 + 0.008264462808 = 4.008264462808 0.008264462808 + 0.1818181818t + t2 = 4.008264462808 Factor a perfect square on the left side: (t + 0.0909090909)(t + 0.0909090909) = 4.008264462808 Calculate the square root of the right side: 2.00206505 Break this problem into two subproblems by setting (t + 0.0909090909) equal to 2.00206505 and -2.00206505.Subproblem 1
t + 0.0909090909 = 2.00206505 Simplifying t + 0.0909090909 = 2.00206505 Reorder the terms: 0.0909090909 + t = 2.00206505 Solving 0.0909090909 + t = 2.00206505 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.0909090909' to each side of the equation. 0.0909090909 + -0.0909090909 + t = 2.00206505 + -0.0909090909 Combine like terms: 0.0909090909 + -0.0909090909 = 0.0000000000 0.0000000000 + t = 2.00206505 + -0.0909090909 t = 2.00206505 + -0.0909090909 Combine like terms: 2.00206505 + -0.0909090909 = 1.9111559591 t = 1.9111559591 Simplifying t = 1.9111559591Subproblem 2
t + 0.0909090909 = -2.00206505 Simplifying t + 0.0909090909 = -2.00206505 Reorder the terms: 0.0909090909 + t = -2.00206505 Solving 0.0909090909 + t = -2.00206505 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.0909090909' to each side of the equation. 0.0909090909 + -0.0909090909 + t = -2.00206505 + -0.0909090909 Combine like terms: 0.0909090909 + -0.0909090909 = 0.0000000000 0.0000000000 + t = -2.00206505 + -0.0909090909 t = -2.00206505 + -0.0909090909 Combine like terms: -2.00206505 + -0.0909090909 = -2.0929741409 t = -2.0929741409 Simplifying t = -2.0929741409Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.9111559591, -2.0929741409}
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