Question

Solve by using square root:
4(x-1)^2+2=10

Answer 1

`4(x-1)^2+2=10 \\ 4(x-1)^2=8\\ (x-1)^2=2\\ x-1=-\sqrt2 \vee x-1=\sqrt2\\ x=1-\sqrt2 \vee x=1+\sqrt2`

Answer 2

`4(x-1)^2+2=10\\\\4(x^2-2x+1)+2-10=0\\\\4 x^2-8x+4+2-10=0\\\\4 x^2-8x-4=0\ \ / :4\\\\x^2-2x-1=0\\\\x_(1)=(-b-√(b^2-4ac))/(2a)=(2-√( (-2)^2-4*1*(-1)))/(2 )=(2-√( 8))/(2 )=(2- √( 4*2))/(2 )=\\\\=(2-√( 8))/(2 )=(2(1- √( 2)))/(2 )=1- √( 2)\\\\x_(2)=(-b+√(b^2-4ac))/(2a)=(2+√( (-2)^2-4*1*(-1)))/(2 )=(2(1+ √( 2)))/(2 )=1+ √( 2)`


`Answer:\ x=1- √(2)\ \ or\ \ x= 1+ √( 2)`