SOLUTION: If G lies on the perpendicular bisector of segment AB, AG = +3x, and BG= -10x+140, find AG. I know that AG=BG, and I need help solving this equation... x^2+3x = -10x+140 I g

Question 202429: If G lies on the perpendicular bisector of segment AB, AG = +3x, and
BG= -10x+140, find AG.
I know that AG=BG, and I need help solving this equation... x^2+3x = -10x+140
I got it down to x^2+13x = 140 and I don't know where to go from here.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
I'm not sure that you have the right equation (I don't have access to the drawing), but here's how you would solve it.

Start with the given equation.

Get all terms to the left side.

Combine like terms.

Notice that the quadratic is in the form of where , , and

Let's use the quadratic formula to solve for "x":

Start with the quadratic formula

Plug in , , and

Square to get .

Multiply to get

Rewrite as

Add to 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 solutions are or

Note: If you only need the positive solution, then just ignore
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