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Simplifying x2 + -10x + -92 = 0 Reorder the terms: -92 + -10x + x2 = 0 Solving -92 + -10x + 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 + -10x + 92 + x2 = 0 + 92 Reorder the terms: -92 + 92 + -10x + x2 = 0 + 92 Combine like terms: -92 + 92 = 0 0 + -10x + x2 = 0 + 92 -10x + x2 = 0 + 92 Combine like terms: 0 + 92 = 92 -10x + x2 = 92 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 92 + 25 Reorder the terms: 25 + -10x + x2 = 92 + 25 Combine like terms: 92 + 25 = 117 25 + -10x + x2 = 117 Factor a perfect square on the left side: (x + -5)(x + -5) = 117 Calculate the square root of the right side: 10.816653826 Break this problem into two subproblems by setting (x + -5) equal to 10.816653826 and -10.816653826.Subproblem 1
x + -5 = 10.816653826 Simplifying x + -5 = 10.816653826 Reorder the terms: -5 + x = 10.816653826 Solving -5 + x = 10.816653826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 10.816653826 + 5 Combine like terms: -5 + 5 = 0 0 + x = 10.816653826 + 5 x = 10.816653826 + 5 Combine like terms: 10.816653826 + 5 = 15.816653826 x = 15.816653826 Simplifying x = 15.816653826Subproblem 2
x + -5 = -10.816653826 Simplifying x + -5 = -10.816653826 Reorder the terms: -5 + x = -10.816653826 Solving -5 + x = -10.816653826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -10.816653826 + 5 Combine like terms: -5 + 5 = 0 0 + x = -10.816653826 + 5 x = -10.816653826 + 5 Combine like terms: -10.816653826 + 5 = -5.816653826 x = -5.816653826 Simplifying x = -5.816653826Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.816653826, -5.816653826}
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