Solve and check 3x Squareroot 6 9x 2Solutiongiven 3x 69x

Solve (and check!) 3x + Squareroot 6 - 9x = 2

Solution

given 3x +(6-9x) =2

=>3x -2 =-(6-9x)

squaring on both sides

=>(3x -2)² =(6-9x)

=>(9x² -12x+4) =(6-9x)

=>9x² -3x =2

=>x² -(1_/3)x =(2_/9)

=>x² -(1_/3)x+(1_/6)² =(2_/9)+(1_/6)²

=>(x -(1_/6))² =(2_/9)+(1_/36)

=>(x -(1_/6))² =(1_/4)

=>(x -(1_/6)) =-(1_/2),(x -(1_/6)) =(1_/2)

=>x =(1_/6)-(1_/2),x =(1_/6)+(1_/2)

=>x =-(1_/3),x =(2_/3)

so solutions are x =-(1_/3),(2_/3)

check:

x =-(1_/3),3x +(6-9x) =2

=>3(-(1_/3)) +(6-9(-(1_/3))) =2

=>-1 +9 =2

=>-1+3=2

=>2=2 =>true

x =(2_/3),3x +(6-9x) =2

=>3(2_/3) +(6-9(2_/3)) =2

=>2 +(6-6) =2

=>2+0=2

=>2=2 => true