x^2 6x-1=0

solve by completing the square.

x² + 6x + 1 = 0 the third term of the square is 9, then replace 1 with (9 - 8): x² + 6x + 9 - 8 = 0 → (x² + 6x + 9) - 8 = 0 → factoring the rising square: (x + 3)² - 8 = 0 → finally, factor the left side, viewing it as a difference between two squares, yielding: (x + 3)² - (√8)² = 0 → [(x + 3) + (√8)][(x + 3) - (√8)] = 0 → (as you know, √8 = √(4)2 = 2√2) (x + 3 + 2√2)(x + 3 - 2√2) = 0 → rewrite it in the (x - a)(x - b) form as: [x - (-3 - 2√2)][x - (-3 + 2√2)] = 0 → thus the required solutions are: [x - (-3 - 2√2)] = 0 → x = - 3 - 2√2 and [x - (-3 + 2√2)] = 0 → x = - 3 + 2√2

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