1.5(x^2-2)=3(x^2+x)2.(x-2)^2=(2x+3)^23.(x-2)(x-3)=124.2x+6=(x+3)^25.2y^2+4y=y+2

Question

1.5(x^2-2)=3(x^2+x)
2.(x-2)^2 = (2x+3)^2
3.(x-2)(x-3)=12
4.2x+6=(x+3)^2
5.2y^2+4y=y+2

Answer 1

1.5(x^2-2)=3(x^2+x)
5x^2-10=3x^2+3x
2x^2-3x-10=0
x^2-3/2x-5=0
x^2-3/2x+9/16-9/16-5=0
(x-3/4)^2-89/16=0
(x-3/4+√89/4)(x-3/4-√89/4)=0
x=-3/4-√89/4 or x=-3/4+√89/4
2.(x-2)^2 = (2x+3)^2
(x-2)^2 -(2x+3)^2=0
[(x-2)-(2x+3)][(x-2)+(2x+3)]=0
(-x-5)(3x+1)=0
-(x+5)(3x+1)=0
(x+5)(3x+1)=0
x=-5 or x=-1/3
3.(x-2)(x-3)=12
x^2-5x+6=12
x^2-5x-6=0
(x-6)(x+1)=0
x=6 or x=-1
4.2x+6=(x+3)^2
x^2+6x+9=2x+6
x^2+4x+3=0
(x+3)(x+1)=0
x=-3 or x=-1
5.2y^2+4y=y+2
2y^2+3y-2=0
(2y-1)(y+2)=0
y=1/2 or y=-2