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Simplifying 11x2 + -24 = 8x Reorder the terms: -24 + 11x2 = 8x Solving -24 + 11x2 = 8x Solving for variable 'x'. Reorder the terms: -24 + -8x + 11x2 = 8x + -8x Combine like terms: 8x + -8x = 0 -24 + -8x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -2.181818182 + -0.7272727273x + x2 = 0 Move the constant term to the right: Add '2.181818182' to each side of the equation. -2.181818182 + -0.7272727273x + 2.181818182 + x2 = 0 + 2.181818182 Reorder the terms: -2.181818182 + 2.181818182 + -0.7272727273x + x2 = 0 + 2.181818182 Combine like terms: -2.181818182 + 2.181818182 = 0.000000000 0.000000000 + -0.7272727273x + x2 = 0 + 2.181818182 -0.7272727273x + x2 = 0 + 2.181818182 Combine like terms: 0 + 2.181818182 = 2.181818182 -0.7272727273x + x2 = 2.181818182 The x term is -0.7272727273x. Take half its coefficient (-0.3636363637). Square it (0.1322314050) and add it to both sides. Add '0.1322314050' to each side of the equation. -0.7272727273x + 0.1322314050 + x2 = 2.181818182 + 0.1322314050 Reorder the terms: 0.1322314050 + -0.7272727273x + x2 = 2.181818182 + 0.1322314050 Combine like terms: 2.181818182 + 0.1322314050 = 2.314049587 0.1322314050 + -0.7272727273x + x2 = 2.314049587 Factor a perfect square on the left side: (x + -0.3636363637)(x + -0.3636363637) = 2.314049587 Calculate the square root of the right side: 1.521200048 Break this problem into two subproblems by setting (x + -0.3636363637) equal to 1.521200048 and -1.521200048.Subproblem 1
x + -0.3636363637 = 1.521200048 Simplifying x + -0.3636363637 = 1.521200048 Reorder the terms: -0.3636363637 + x = 1.521200048 Solving -0.3636363637 + x = 1.521200048 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3636363637' to each side of the equation. -0.3636363637 + 0.3636363637 + x = 1.521200048 + 0.3636363637 Combine like terms: -0.3636363637 + 0.3636363637 = 0.0000000000 0.0000000000 + x = 1.521200048 + 0.3636363637 x = 1.521200048 + 0.3636363637 Combine like terms: 1.521200048 + 0.3636363637 = 1.8848364117 x = 1.8848364117 Simplifying x = 1.8848364117Subproblem 2
x + -0.3636363637 = -1.521200048 Simplifying x + -0.3636363637 = -1.521200048 Reorder the terms: -0.3636363637 + x = -1.521200048 Solving -0.3636363637 + x = -1.521200048 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3636363637' to each side of the equation. -0.3636363637 + 0.3636363637 + x = -1.521200048 + 0.3636363637 Combine like terms: -0.3636363637 + 0.3636363637 = 0.0000000000 0.0000000000 + x = -1.521200048 + 0.3636363637 x = -1.521200048 + 0.3636363637 Combine like terms: -1.521200048 + 0.3636363637 = -1.1575636843 x = -1.1575636843 Simplifying x = -1.1575636843Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.8848364117, -1.1575636843}
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