Step-by-step explanation:
Hey there!!
The equation is;
[tex] {x}^{2} - 6x + 7 = 0[/tex]
Now, Comparing it with ax^2 + bx + c = 0. we get;
a = 1, b= -6 and c = 7
Use quadratic formula.
[tex]x = \frac{ - b + - \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]
Put all values.
[tex]x = \frac{ + 6 + - \sqrt{( { - 6)}^{2} - 4 \times 1 \times 7} }{2 \times 1} [/tex]
Simplify them.
[tex]x = \frac{6 + - \sqrt{36 - 28} }{2} [/tex]
[tex]x = \frac{ 6 + - \sqrt{8} }{2} [/tex]
[tex]x = \frac{6 + - 2 \sqrt{2} }{2} [/tex]
Taking positive (+).
[tex]x = \frac{6 + 2 \sqrt{2} }{2} [/tex]
Simplifying them.
[tex]x = \frac{2(3 + \sqrt{2} )}{2} [/tex]
[tex]x = 3 + \sqrt{2} [/tex]
Now, Taking negative (-).
[tex]x = \frac{6 - 2 \sqrt{2} }{2} [/tex]
Simplifying them.
[tex]x = \frac{2(3 - \sqrt{2} )}{2} [/tex]
[tex]x = 3 - \sqrt{2} [/tex]
Therefore the answer is;
[tex]x = 3 + \sqrt{2} \: and \: 3 - \sqrt{2} [/tex]
Hope it helps...
