Solve the equation (2x-3)^2+(x+2)^2=10+5x^2

To solve the equation, we'll have to expand the squares
from the left side, first.

To expand the squares, we'll use
the formula:

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

We'll expand the square:
(2x-3)^2

(2x-3)^2 = (2x)^2 - 2*2x*3 +
3^2

(2x-3)^2 = 4x^2 - 12x +
9

We'll expand
(x+2)^2:

(x+2)^2 = x^2 + 2*x*2 +
2^2

(x+2)^2 = x^2 + 4x +
4

We'll re-write the
equation:

4x^2 - 12x + 9 + x^2 + 4x + 4 =
10+5x^2

We'll subtract both sides
(10+5x^2):

4x^2 - 12x + 9 + x^2 + 4x + 4 - 10 - 5x^2 =
0

We'll combine and eliminate like
terms:

-8x + 3 = 0

We'll
subtract 3 both sides:

-8x =
-3

We'll divide by -8:

x =
-3/-8

x = 3/8

x
= 0.375