Solve for x : (x+1)^2 = 2x^2 - 5x + 11

The first step is to expand the square from the left side,
using the formula:

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

(x+1)^2 = x^2 + 2x +
1

We'll re-write the given
equation:

x^2 + 2x + 1 = 2x^2 - 5x +
11

We'll move all terms to the right
side:

0 = 2x^2 - x^2 - 5x - 2x + 11 -
1

We'll combine like terms and we'll use symmetrical
property:

x^2 - 7x + 10 =
0

We'll apply quadratic
formula:

x1 = [7 + sqrt(49 -
40)]/2

x1 = (7+sqrt9)/2

x1 =
(7+3)/2

x1 = 5

x2 =
(7-3)/2

x2 =
2

The quadratic equation has the following
solutions: x1 = 5 and x2 = 2.