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Simplifying x2 + -6x + -23 = 0 Reorder the terms: -23 + -6x + x2 = 0 Solving -23 + -6x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '23' to each side of the equation. -23 + -6x + 23 + x2 = 0 + 23 Reorder the terms: -23 + 23 + -6x + x2 = 0 + 23 Combine like terms: -23 + 23 = 0 0 + -6x + x2 = 0 + 23 -6x + x2 = 0 + 23 Combine like terms: 0 + 23 = 23 -6x + x2 = 23 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 23 + 9 Reorder the terms: 9 + -6x + x2 = 23 + 9 Combine like terms: 23 + 9 = 32 9 + -6x + x2 = 32 Factor a perfect square on the left side: (x + -3)(x + -3) = 32 Calculate the square root of the right side: 5.656854249 Break this problem into two subproblems by setting (x + -3) equal to 5.656854249 and -5.656854249.Subproblem 1
x + -3 = 5.656854249 Simplifying x + -3 = 5.656854249 Reorder the terms: -3 + x = 5.656854249 Solving -3 + x = 5.656854249 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 5.656854249 + 3 Combine like terms: -3 + 3 = 0 0 + x = 5.656854249 + 3 x = 5.656854249 + 3 Combine like terms: 5.656854249 + 3 = 8.656854249 x = 8.656854249 Simplifying x = 8.656854249Subproblem 2
x + -3 = -5.656854249 Simplifying x + -3 = -5.656854249 Reorder the terms: -3 + x = -5.656854249 Solving -3 + x = -5.656854249 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -5.656854249 + 3 Combine like terms: -3 + 3 = 0 0 + x = -5.656854249 + 3 x = -5.656854249 + 3 Combine like terms: -5.656854249 + 3 = -2.656854249 x = -2.656854249 Simplifying x = -2.656854249Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.656854249, -2.656854249}
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