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Simplifying 11x2 + -24x + -261 = 0 Reorder the terms: -261 + -24x + 11x2 = 0 Solving -261 + -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'. -23.72727273 + -2.181818182x + x2 = 0 Move the constant term to the right: Add '23.72727273' to each side of the equation. -23.72727273 + -2.181818182x + 23.72727273 + x2 = 0 + 23.72727273 Reorder the terms: -23.72727273 + 23.72727273 + -2.181818182x + x2 = 0 + 23.72727273 Combine like terms: -23.72727273 + 23.72727273 = 0.00000000 0.00000000 + -2.181818182x + x2 = 0 + 23.72727273 -2.181818182x + x2 = 0 + 23.72727273 Combine like terms: 0 + 23.72727273 = 23.72727273 -2.181818182x + x2 = 23.72727273 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 = 23.72727273 + 1.190082645 Reorder the terms: 1.190082645 + -2.181818182x + x2 = 23.72727273 + 1.190082645 Combine like terms: 23.72727273 + 1.190082645 = 24.917355375 1.190082645 + -2.181818182x + x2 = 24.917355375 Factor a perfect square on the left side: (x + -1.090909091)(x + -1.090909091) = 24.917355375 Calculate the square root of the right side: 4.991728696 Break this problem into two subproblems by setting (x + -1.090909091) equal to 4.991728696 and -4.991728696.Subproblem 1
x + -1.090909091 = 4.991728696 Simplifying x + -1.090909091 = 4.991728696 Reorder the terms: -1.090909091 + x = 4.991728696 Solving -1.090909091 + x = 4.991728696 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 = 4.991728696 + 1.090909091 Combine like terms: -1.090909091 + 1.090909091 = 0.000000000 0.000000000 + x = 4.991728696 + 1.090909091 x = 4.991728696 + 1.090909091 Combine like terms: 4.991728696 + 1.090909091 = 6.082637787 x = 6.082637787 Simplifying x = 6.082637787Subproblem 2
x + -1.090909091 = -4.991728696 Simplifying x + -1.090909091 = -4.991728696 Reorder the terms: -1.090909091 + x = -4.991728696 Solving -1.090909091 + x = -4.991728696 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 = -4.991728696 + 1.090909091 Combine like terms: -1.090909091 + 1.090909091 = 0.000000000 0.000000000 + x = -4.991728696 + 1.090909091 x = -4.991728696 + 1.090909091 Combine like terms: -4.991728696 + 1.090909091 = -3.900819605 x = -3.900819605 Simplifying x = -3.900819605Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.082637787, -3.900819605}
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