X2=13x+42=0
Use the quadratic formula to solve
You said "Use the quadratic formula..." so that
must be x^2. The problem with this is the second
term: is it positive or negative. The solution
is different for the two possibilities.
First, assuming that the term is +13x:
-b ± sqrt(b^2 - 4*a*c)
x = ----------------------------
2a
-13 ± sqrt(13^2 - 4*1*42)
x = ---------------------------------
2(1)
-13 ± sqrt(169 - 168)
x = ----------------------------
2
-13 ± sqrt(1)
x = ------------------
2
-13 ± 1
x = ------------
2
-13 + 1 -13 - 1
x = ------------ and x = ------------
2 2
-12 -14
x = ------- and x = -------
2 2
x = -6 and x = -7
I won't go through the entire process again, but
if we assume the second term is -13x, the major
change for the quadratic equation is the -b. Instead
of -13, it is now +13. The result is as follows:
13 ± 1
x = ------------
2
13 + 1 13 - 1
x = ------------ and x = ------------
2 2
14 12
x = ------- and x = -------
2 2
x = 7 and x = 6
As you can see, the values of x change from negative to positive.