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Simplifying x2 + -3x + -92 = 0 Reorder the terms: -92 + -3x + x2 = 0 Solving -92 + -3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '92' to each side of the equation. -92 + -3x + 92 + x2 = 0 + 92 Reorder the terms: -92 + 92 + -3x + x2 = 0 + 92 Combine like terms: -92 + 92 = 0 0 + -3x + x2 = 0 + 92 -3x + x2 = 0 + 92 Combine like terms: 0 + 92 = 92 -3x + x2 = 92 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 92 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 92 + 2.25 Combine like terms: 92 + 2.25 = 94.25 2.25 + -3x + x2 = 94.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 94.25 Calculate the square root of the right side: 9.708243919 Break this problem into two subproblems by setting (x + -1.5) equal to 9.708243919 and -9.708243919.Subproblem 1
x + -1.5 = 9.708243919 Simplifying x + -1.5 = 9.708243919 Reorder the terms: -1.5 + x = 9.708243919 Solving -1.5 + x = 9.708243919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 9.708243919 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 9.708243919 + 1.5 x = 9.708243919 + 1.5 Combine like terms: 9.708243919 + 1.5 = 11.208243919 x = 11.208243919 Simplifying x = 11.208243919Subproblem 2
x + -1.5 = -9.708243919 Simplifying x + -1.5 = -9.708243919 Reorder the terms: -1.5 + x = -9.708243919 Solving -1.5 + x = -9.708243919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -9.708243919 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -9.708243919 + 1.5 x = -9.708243919 + 1.5 Combine like terms: -9.708243919 + 1.5 = -8.208243919 x = -8.208243919 Simplifying x = -8.208243919Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.208243919, -8.208243919}
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