/sci/ - Science & Math

How can I solve this system of equations? I've tried all night and all day but I get nowhere every time.
[math]a+b+c+d=100[/math],

[math]a^2=b^2+c^2+d^2[/math], and

[math]d=c+1[/math],

I've reduced it down to two equations by subbing in the value given for [math]c[/math].

[math]a+b+2c=99[/math], and

[math]a^2=b^2+2c^2+2c+1[/math].

I've tried rearranging the first equation for [math]a[/math] and squaring the RHS and letting it equal the second equation's RHS. It gets messy with non-linear terms.

How do I do this? I know there are solutions because Wolfram. Also I'm not that retarded at math so feel free to be technical. PS: I don't want to graph them and find intersections. Pic unrelated.