quadratic equation by completing the squares x²-2x-2=0
Answer (1)
Answer: x = 1 + [tex]\sqrt{3}[/tex], and x = 1 -[tex]\sqrt{3}[/tex]Step-by-step explanation:We start with x²- 2x -2 = 0Move the constant: x²- 2x = +2Now take half the coefficient of x, square it, and add to both sides: (1/2)(-1) = -1 (-1)^2 = 1x²- 2x + 1 = +2 + 1x²- 2x + 1 = 3Note that x²- 2x + 1 can be factored into: (x - 1)(x-1) or (x-1)^2Now we can write: (x-1)^2 = 3(x-1) = ±[tex]\sqrt{3}[/tex]x = 1 ±[tex]\sqrt{3}[/tex]So the two solutions are x = 1 + [tex]\sqrt{3}[/tex], and x = 1 -[tex]\sqrt{3}[/tex]
