For this case we have the following functions:
[tex]f (x) = x ^ 2-3x + 7\\g (x) = x + 3[/tex]
Equalizing we have:
[tex]x ^ 2-3x + 7 = x + 3\\x ^ 2-3x-x + 7-3 = 0\\x ^ 2-4x + 4 = 0[/tex]
To solve we factorize, that is, we look for two numbers that when multiplied give a result of 4 and when added together give a result of -4. These numbers are -2 and -2.
[tex]-2-2 = -4\\(-2) * (- 2) = 4[/tex]
Thus, we have:
[tex](x-2) (x-2) = 0\\(x-2) ^ 2 = 0[/tex]
So, the solution is[tex]x = 2[/tex]
Answer:
[tex]x=2[/tex]
