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

Algebra ->  Triangles -> 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      Log On


   

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) About Me  (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.




x%5E2%2B3x=-10x%2B140 Start with the given equation.


x%5E2%2B3x%2B10x-140=0 Get all terms to the left side.


x%5E2%2B13x-140=0 Combine like terms.


Notice that the quadratic x%5E2%2B13x-140 is in the form of Ax%5E2%2BBx%2BC where A=1, B=13, and C=-140


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


x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


x+=+%28-%2813%29+%2B-+sqrt%28+%2813%29%5E2-4%281%29%28-140%29+%29%29%2F%282%281%29%29 Plug in A=1, B=13, and C=-140


x+=+%28-13+%2B-+sqrt%28+169-4%281%29%28-140%29+%29%29%2F%282%281%29%29 Square 13 to get 169.


x+=+%28-13+%2B-+sqrt%28+169--560+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-140%29 to get -560


x+=+%28-13+%2B-+sqrt%28+169%2B560+%29%29%2F%282%281%29%29 Rewrite sqrt%28169--560%29 as sqrt%28169%2B560%29


x+=+%28-13+%2B-+sqrt%28+729+%29%29%2F%282%281%29%29 Add 169 to 560 to get 729


x+=+%28-13+%2B-+sqrt%28+729+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%28-13+%2B-+27%29%2F%282%29 Take the square root of 729 to get 27.


x+=+%28-13+%2B+27%29%2F%282%29 or x+=+%28-13+-+27%29%2F%282%29 Break up the expression.


x+=+%2814%29%2F%282%29 or x+=++%28-40%29%2F%282%29 Combine like terms.


x+=+7 or x+=+-20 Simplify.


So the solutions are x+=+7 or x+=+-20

Note: If you only need the positive solution, then just ignore x+=+-20