Answer:
[tex]x^2-6x=-7[/tex]
[tex]x^2-6x+9=-7+9[/tex]
[tex](x-3)^2=2[/tex]
[tex]\sqrt{(x-3)^2}=\pm\sqrt{2}[/tex]
[tex](x-3)=\pm\sqrt{2}[/tex]
[tex]x-3=3\pm\sqrt{2}[/tex]
Step-by-step explanation:
The given quadratic equation is
[tex]x^2-6x+7=0[/tex]
Subtract 7 from both sides.
[tex]x^2-6x=-7[/tex] ...(1)
If an expression is [tex]x^2+bx[/tex], then we add [tex](\frac{b}{2})^2[/tex] to make it perfect square.
[tex](\frac{b}{2})^2=(\frac{-6}{2})^2=9[/tex]
Add 9 on both sides in equation (1).
[tex]x^2-6x+9=-7+9[/tex]
[tex](x-3)^2=2[/tex] [tex][\because (a-b)^2=a^2-2ab+b^2][/tex]
Taking square root on both sides.
[tex]\sqrt{(x-3)^2}=\pm\sqrt{2}[/tex]
[tex](x-3)=\pm\sqrt{2}[/tex]
Add 3 on both sides.
[tex]x-3=3\pm\sqrt{2}[/tex]
Therefore, the correct order is F, A, D, C, E and B.
