# A Solution To A Question On Math Stack Exchange: Where Have I Gone Wrong?

I came across this problem on math stack exchange and tried to solve it myself: The position of a ladder leaning against a wall and touching a box under it.

What I did was set up 2 equations

$$(x+1)^2+(y+1)^2=4^2$$

$$x^2+1^2=(4-(1+y)^2)^2$$

Then by similar triangles:

$$x/(x+1)=1/(1+y)$$

I took $$(x+1)^2+(y+1)^2=4^2$$ then solved for 1+y to get $$sqrt(-x^2-2x-15)$$

I then plugged this back into the original and got

$$x+1/x = 1/(-x^2-2x-15)$$

However, my equation gives complex solutions. So where have I gone wrong? How can I get to the right solution using these 2 equations?

• Please choose a more descriptive title. Thanks. – user370967 Nov 4 '18 at 8:37

The problem is in the step in which you solve the equation $$(x+1)^2+(y+1)^2=4^2$$. You should have obtained$$y+1=\pm\sqrt{15-x^2-2x}.$$