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Simplifying 4t + -4 = 11t2 + -32 Reorder the terms: -4 + 4t = 11t2 + -32 Reorder the terms: -4 + 4t = -32 + 11t2 Solving -4 + 4t = -32 + 11t2 Solving for variable 't'. Reorder the terms: -4 + 32 + 4t + -11t2 = -32 + 11t2 + 32 + -11t2 Combine like terms: -4 + 32 = 28 28 + 4t + -11t2 = -32 + 11t2 + 32 + -11t2 Reorder the terms: 28 + 4t + -11t2 = -32 + 32 + 11t2 + -11t2 Combine like terms: -32 + 32 = 0 28 + 4t + -11t2 = 0 + 11t2 + -11t2 28 + 4t + -11t2 = 11t2 + -11t2 Combine like terms: 11t2 + -11t2 = 0 28 + 4t + -11t2 = 0 Begin completing the square. Divide all terms by -11 the coefficient of the squared term: Divide each side by '-11'. -2.545454545 + -0.3636363636t + t2 = 0 Move the constant term to the right: Add '2.545454545' to each side of the equation. -2.545454545 + -0.3636363636t + 2.545454545 + t2 = 0 + 2.545454545 Reorder the terms: -2.545454545 + 2.545454545 + -0.3636363636t + t2 = 0 + 2.545454545 Combine like terms: -2.545454545 + 2.545454545 = 0.000000000 0.000000000 + -0.3636363636t + t2 = 0 + 2.545454545 -0.3636363636t + t2 = 0 + 2.545454545 Combine like terms: 0 + 2.545454545 = 2.545454545 -0.3636363636t + t2 = 2.545454545 The t term is -0.3636363636t. Take half its coefficient (-0.1818181818). Square it (0.03305785123) and add it to both sides. Add '0.03305785123' to each side of the equation. -0.3636363636t + 0.03305785123 + t2 = 2.545454545 + 0.03305785123 Reorder the terms: 0.03305785123 + -0.3636363636t + t2 = 2.545454545 + 0.03305785123 Combine like terms: 2.545454545 + 0.03305785123 = 2.57851239623 0.03305785123 + -0.3636363636t + t2 = 2.57851239623 Factor a perfect square on the left side: (t + -0.1818181818)(t + -0.1818181818) = 2.57851239623 Calculate the square root of the right side: 1.605774703 Break this problem into two subproblems by setting (t + -0.1818181818) equal to 1.605774703 and -1.605774703.Subproblem 1
t + -0.1818181818 = 1.605774703 Simplifying t + -0.1818181818 = 1.605774703 Reorder the terms: -0.1818181818 + t = 1.605774703 Solving -0.1818181818 + t = 1.605774703 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.1818181818' to each side of the equation. -0.1818181818 + 0.1818181818 + t = 1.605774703 + 0.1818181818 Combine like terms: -0.1818181818 + 0.1818181818 = 0.0000000000 0.0000000000 + t = 1.605774703 + 0.1818181818 t = 1.605774703 + 0.1818181818 Combine like terms: 1.605774703 + 0.1818181818 = 1.7875928848 t = 1.7875928848 Simplifying t = 1.7875928848Subproblem 2
t + -0.1818181818 = -1.605774703 Simplifying t + -0.1818181818 = -1.605774703 Reorder the terms: -0.1818181818 + t = -1.605774703 Solving -0.1818181818 + t = -1.605774703 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.1818181818' to each side of the equation. -0.1818181818 + 0.1818181818 + t = -1.605774703 + 0.1818181818 Combine like terms: -0.1818181818 + 0.1818181818 = 0.0000000000 0.0000000000 + t = -1.605774703 + 0.1818181818 t = -1.605774703 + 0.1818181818 Combine like terms: -1.605774703 + 0.1818181818 = -1.4239565212 t = -1.4239565212 Simplifying t = -1.4239565212Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.7875928848, -1.4239565212}
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