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Simplifying 11x2 + -24x + -4 = 0 Reorder the terms: -4 + -24x + 11x2 = 0 Solving -4 + -24x + 11x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.3636363636 + -2.181818182x + x2 = 0 Move the constant term to the right: Add '0.3636363636' to each side of the equation. -0.3636363636 + -2.181818182x + 0.3636363636 + x2 = 0 + 0.3636363636 Reorder the terms: -0.3636363636 + 0.3636363636 + -2.181818182x + x2 = 0 + 0.3636363636 Combine like terms: -0.3636363636 + 0.3636363636 = 0.0000000000 0.0000000000 + -2.181818182x + x2 = 0 + 0.3636363636 -2.181818182x + x2 = 0 + 0.3636363636 Combine like terms: 0 + 0.3636363636 = 0.3636363636 -2.181818182x + x2 = 0.3636363636 The x term is -2.181818182x. Take half its coefficient (-1.090909091). Square it (1.190082645) and add it to both sides. Add '1.190082645' to each side of the equation. -2.181818182x + 1.190082645 + x2 = 0.3636363636 + 1.190082645 Reorder the terms: 1.190082645 + -2.181818182x + x2 = 0.3636363636 + 1.190082645 Combine like terms: 0.3636363636 + 1.190082645 = 1.5537190086 1.190082645 + -2.181818182x + x2 = 1.5537190086 Factor a perfect square on the left side: (x + -1.090909091)(x + -1.090909091) = 1.5537190086 Calculate the square root of the right side: 1.246482655 Break this problem into two subproblems by setting (x + -1.090909091) equal to 1.246482655 and -1.246482655.Subproblem 1
x + -1.090909091 = 1.246482655 Simplifying x + -1.090909091 = 1.246482655 Reorder the terms: -1.090909091 + x = 1.246482655 Solving -1.090909091 + x = 1.246482655 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.090909091' to each side of the equation. -1.090909091 + 1.090909091 + x = 1.246482655 + 1.090909091 Combine like terms: -1.090909091 + 1.090909091 = 0.000000000 0.000000000 + x = 1.246482655 + 1.090909091 x = 1.246482655 + 1.090909091 Combine like terms: 1.246482655 + 1.090909091 = 2.337391746 x = 2.337391746 Simplifying x = 2.337391746Subproblem 2
x + -1.090909091 = -1.246482655 Simplifying x + -1.090909091 = -1.246482655 Reorder the terms: -1.090909091 + x = -1.246482655 Solving -1.090909091 + x = -1.246482655 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.090909091' to each side of the equation. -1.090909091 + 1.090909091 + x = -1.246482655 + 1.090909091 Combine like terms: -1.090909091 + 1.090909091 = 0.000000000 0.000000000 + x = -1.246482655 + 1.090909091 x = -1.246482655 + 1.090909091 Combine like terms: -1.246482655 + 1.090909091 = -0.155573564 x = -0.155573564 Simplifying x = -0.155573564Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.337391746, -0.155573564}
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