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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 = 5.816653826 x = 5.816653826 Simplifying x = 5.816653826Subproblem 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 = -15.816653826 x = -15.816653826 Simplifying x = -15.816653826Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.816653826, -15.816653826}
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