SOLUTION: I need to find x, AB, and BC, where A, B, and C are points on a line...A is the leftmost point, C is the rightmost point, and B is in between A and C (not necessarily the midway)

Question 156831: I need to find x, AB, and BC, where A, B, and C are points on a line...A is the leftmost point, C is the rightmost point, and B is in between A and C (not necessarily the midway)
AB = square root (3x +4)
BC = x-6
AC = 6
I was able to write out sqrt(3x+4) + x - 6 = 6, then simplifies to SQRT (3x+4) + x = 12. I don't understand how to eliminate the square root in these radical equations.
Please help.
Thank you.

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the given equation.

Add 6 to both sides.

Subtract "x" from both sides.

Square both sides to eliminate the square root

FOIL

Subtract from both sides. Subtract from both sides.

Combine like terms.

Notice we have a quadratic equation in the form of where , , and

Let's use the quadratic formula to solve for x

Start with the quadratic formula

Plug in , , and

Negate to get .

Square to get .

Multiply to get

Subtract from to get

Multiply and to get .

Take the square root of to get .

or Break up the expression.

or Combine like terms.

or Simplify.

So the possible answers are or

However, if you plug back into the original equation, you'll find that it doesn't work.

So the only solution is

Now plug in into AB, BC, and AC

So the lengths are , , and

Check:

Remember, AB+BC=AC

AB+BC=AC ... Start with the given equation

5+1=6 ... Plug in , , and

6=6 ... Add Since this equation is true, this verifies the answer.
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