What is 2square root 3X + 7 - 4 = X + 1?

Question

The problem has a square root. I could not type it in the title section. See the problem below.

Can you please show & explain the steps in solving? Thank you.

2 3X + 7 - 4 = X + 1?

Answer 1

Assuming the square root is just over the 3X.

2√3X +7-4=X+1 <---- collect like terms

2√3X+3=X+1 <------move the +3 over to the other side so need to subtract 3 to both sides

2√3X=X-2 <------now we need to get rid of the square root and to do that we need to square both side

(2√3X)²=(X-2)² <-----on the left side you square the 2 and it get rid of the square root of 3X

4(3X)=(X-2)(X-2) <---- notice there are two (X-2) because it was squared

12X=X²-4X+4 <----- move the 12X over to the right side

0=X²-16X+4

Now we can use the quadratic formula:

X=[-b±√(b²-4ac)]/2a <---- the square root covers b²-4ac

We have the form aX²+bX+c=0 so we can just plug into the quadratic formula:

In our case a=1, b=-16, and c=4

X=[-(-16)±√(16²-4*1*4)]/(2*1)

=[16±√(256-16)]/2

=[16±√240]/2

=[16±4√15]/2

=8±2√15

So,

X=8+2√15 or 8−2√15