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Simplifying 11x2 + 24x + -24 = 0 Reorder the terms: -24 + 24x + 11x2 = 0 Solving -24 + 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'. -2.181818182 + 2.181818182x + x2 = 0 Move the constant term to the right: Add '2.181818182' to each side of the equation. -2.181818182 + 2.181818182x + 2.181818182 + x2 = 0 + 2.181818182 Reorder the terms: -2.181818182 + 2.181818182 + 2.181818182x + x2 = 0 + 2.181818182 Combine like terms: -2.181818182 + 2.181818182 = 0.000000000 0.000000000 + 2.181818182x + x2 = 0 + 2.181818182 2.181818182x + x2 = 0 + 2.181818182 Combine like terms: 0 + 2.181818182 = 2.181818182 2.181818182x + x2 = 2.181818182 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 = 2.181818182 + 1.190082645 Reorder the terms: 1.190082645 + 2.181818182x + x2 = 2.181818182 + 1.190082645 Combine like terms: 2.181818182 + 1.190082645 = 3.371900827 1.190082645 + 2.181818182x + x2 = 3.371900827 Factor a perfect square on the left side: (x + 1.090909091)(x + 1.090909091) = 3.371900827 Calculate the square root of the right side: 1.836273625 Break this problem into two subproblems by setting (x + 1.090909091) equal to 1.836273625 and -1.836273625.Subproblem 1
x + 1.090909091 = 1.836273625 Simplifying x + 1.090909091 = 1.836273625 Reorder the terms: 1.090909091 + x = 1.836273625 Solving 1.090909091 + x = 1.836273625 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 = 1.836273625 + -1.090909091 Combine like terms: 1.090909091 + -1.090909091 = 0.000000000 0.000000000 + x = 1.836273625 + -1.090909091 x = 1.836273625 + -1.090909091 Combine like terms: 1.836273625 + -1.090909091 = 0.745364534 x = 0.745364534 Simplifying x = 0.745364534Subproblem 2
x + 1.090909091 = -1.836273625 Simplifying x + 1.090909091 = -1.836273625 Reorder the terms: 1.090909091 + x = -1.836273625 Solving 1.090909091 + x = -1.836273625 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 = -1.836273625 + -1.090909091 Combine like terms: 1.090909091 + -1.090909091 = 0.000000000 0.000000000 + x = -1.836273625 + -1.090909091 x = -1.836273625 + -1.090909091 Combine like terms: -1.836273625 + -1.090909091 = -2.927182716 x = -2.927182716 Simplifying x = -2.927182716Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.745364534, -2.927182716}
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