What is the value of variable x (x+3)^2-2(9x-13)=0 ?

To determine the values of x, we'll have to solve the
quadratic equation.

For this reason, we'll expand the
square and we'll remove the brackets.

We'll expand the
square using the formula:

(a+b)^2 = a^2 + 2ab +
b^2

Now, we'll expand
(x+3)^2:

(x+3)^2 = x^2 + 6x +
9

The equation will
become:

x^2 + 6x + 9 - 18x + 26 =
0

We'll combine like
terms:

x^2 - 12x + 35 =
0

We'll apply quadratic
formula;

x1 = [12+sqrt(144 -
140)]/2

x1 = (12+2)/2

x1 =
7

x2 = (12-2)/2

x2 =
5

The solutions of the equation are {5 ;
7}.