What is the value(s) of x? x^2 = 10x + 16

Well, the first thing is to move the terms from the right
side, to the left side, changing their signs. Since both terms are positive to the right
side, they will become negative, to the left side.

x^2 =
10x + 16

x^2 - 10x - 16 =
0

Now, we'll solve the quadratic equation, using the
quadratic formula.

x1 = [-b+sqrt(b^2 -4ac
)]/2a

x2 = [-b-sqrt(b^2 -4ac
)]/2a

The coefficients a,b,c are the coefficients of the
quadratic: ax^2 + bx + c = 0

We'll identify
a,b,c:

a = 1

b =
-10

c = -16

delta = b^2 -
4ac

delta = 100 + 64

delta =
164

sqrt delta = 2sqrt41

x1 =
(10+2sqrt41)/2

x1 =
5+sqrt41

x2 =
5-sqrt41

The values of x that verify the
expression x^2 = 10x + 16 are {5-sqrt41 ;
5+sqrt41}.