Solving a set of simultaneous equations

I have the following set of simultaneous equations that I want to solve. I'm just confused as to what solver is the best choice!

Can it be even solved?

a = 0.5;
sqrt(x1^2 + a*x1*x2 + a*x1*x3 + a*x1*x4) = 30;
sqrt(a*x2*x1 + x2^2 + a*x2*x3 + a*x2*x4) = 33;
sqrt(a*x3*x1 + a*x3*x2 + x3^2 + a*x3*x4) = 25;
sqrt(a*x4*x1 + a*x4*x2 + a*x4*x3 + x4^2) = 10;

Thank you!

[Alex Sha]

There will be multi-solution if no range limition:

No.	x1	x2	x3	x4
1	-27.5584616528484	-31.4642304277135	-21.2013312551081	42.4667927458073
2	27.5584616528484	31.4642304277135	21.2013312551081	-42.4667927458073
3	21.092393187031	24.5327728282962	15.6460319211707	2.9752314576261
4	-35.124387658461	55.4211403974195	-28.2016268231437	-8.21718324886969
5	35.124387658461	-55.4211403974195	28.2016268231437	8.21718324886969
6	46.8115886629648	-42.6760633957222	-31.4217676113028	18.926670615613
7	-39.7163903825374	49.5555904803269	-32.6637611270595	17.2196122200305
8	39.7163903825374	-49.5555904803269	32.6637611270595	-17.2196122200305
9	-46.8115886629648	42.6760633957222	31.4217676113028	-18.926670615613
10	31.8811243735484	35.9706867855451	-49.7196043306907	6.44640901641614
11	-31.8811243735484	-35.9706867855451	49.7196043306907	-6.44640901641614
12	36.4849054651774	40.6839971426023	-42.3597267431898	-21.95861020684
13	-36.4849054651774	-40.6839971426023	42.3597267431898	21.95861020684
14	53.1637277627363	-38.0038803965751	-26.9964048344445	-7.46949936450619
15	-53.1637277627363	38.0038803965751	26.9964048344445	7.46949936450619

Answer 1

[Torsten]

a = 0.5;
fun =@(x1,x2,x3,x4) [x1^2 + a*x1*x2 + a*x1*x3 + a*x1*x4 - 30^2;...
                     a*x2*x1 + x2^2 + a*x2*x3 + a*x2*x4 - 33^2;...
                     a*x3*x1 + a*x3*x2 + x3^2 + a*x3*x4 - 25^2;...
                     a*x4*x1 + a*x4*x2 + a*x4*x3 + x4^2 - 10^2];
x = fsolve(@(x)fun(x(1),x(2),x(3),x(4)),[1 1 1 1])
fun(x(1),x(2),x(3),x(4))