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

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

(2x-3)^2 + (x+2)^2 = 10+5x^2

open bracktes:

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

Combine like terms:

==> 5x^2 - 8x + 13 = 5x^2 + 10

==> -8x = -3

==> x= 3/8

neela | High School Teacher | (Level 3) Valedictorian

Posted on

To solve

(2x-3)^2+(x+2)^2=10+5x^2

Expand the esxpression and rewrite:

4x^2-12x+9+x^2+4x+4 = 10+5x^2. Collect like terms together on the left.

(4+1-5)x^2 +(-12+4)x +9+4-10 = 0

-8x+3 = 0

-8x = -3

x = -3/-8 =  3/8

x = 3/8

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

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

william1941 | College Teacher | (Level 3) Valedictorian

Posted on

The equation given is : (2x-3)^2+(x+2)^2=10+5x^2 . Solving it,

(2x-3)^2+(x+2)^2=10+5x^2

open the brackets

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

Cancel the common terms

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

=> -8x + 3 =0

=> 8x =3

divide by 3

=> x = 3/8

Therefore x = 3/8