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Simplifying 11x2 + -24x + -44 = 0 Reorder the terms: -44 + -24x + 11x2 = 0 Solving -44 + -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'. -4 + -2.181818182x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -2.181818182x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -2.181818182x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -2.181818182x + x2 = 0 + 4 -2.181818182x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -2.181818182x + x2 = 4 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 = 4 + 1.190082645 Reorder the terms: 1.190082645 + -2.181818182x + x2 = 4 + 1.190082645 Combine like terms: 4 + 1.190082645 = 5.190082645 1.190082645 + -2.181818182x + x2 = 5.190082645 Factor a perfect square on the left side: (x + -1.090909091)(x + -1.090909091) = 5.190082645 Calculate the square root of the right side: 2.278175288 Break this problem into two subproblems by setting (x + -1.090909091) equal to 2.278175288 and -2.278175288.Subproblem 1
x + -1.090909091 = 2.278175288 Simplifying x + -1.090909091 = 2.278175288 Reorder the terms: -1.090909091 + x = 2.278175288 Solving -1.090909091 + x = 2.278175288 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 = 2.278175288 + 1.090909091 Combine like terms: -1.090909091 + 1.090909091 = 0.000000000 0.000000000 + x = 2.278175288 + 1.090909091 x = 2.278175288 + 1.090909091 Combine like terms: 2.278175288 + 1.090909091 = 3.369084379 x = 3.369084379 Simplifying x = 3.369084379Subproblem 2
x + -1.090909091 = -2.278175288 Simplifying x + -1.090909091 = -2.278175288 Reorder the terms: -1.090909091 + x = -2.278175288 Solving -1.090909091 + x = -2.278175288 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 = -2.278175288 + 1.090909091 Combine like terms: -1.090909091 + 1.090909091 = 0.000000000 0.000000000 + x = -2.278175288 + 1.090909091 x = -2.278175288 + 1.090909091 Combine like terms: -2.278175288 + 1.090909091 = -1.187266197 x = -1.187266197 Simplifying x = -1.187266197Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.369084379, -1.187266197}
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