# findroot multiple variables

I have an equation 811*a + 741*b + 1025*c + 752*d = 94508.16372

How can I find the possible roots of a b c and d in specific scopes? I tried FindRoot, it doesn't work since it's not a system of equations.

• For "specific scopes" include constraints as part of the system of equalities or inequalities given to Reduce or Solve or NSolve. Or use FindInstance to get some example solutions. For example, FindInstance[811 a + 741 b + 1025 c + 752 d == 94508.16372, {a, b, c, d}, Reals, 5] Also, FindInstance can take constraints. Commented Jan 22, 2021 at 16:23
• Thanks for help Bob
– YzWu
Commented Jan 22, 2021 at 17:48

As you have 1 equation but 4 variables, the answer will have 3 free variables. The calculation can easily be done by hand. But if, for some reason, you want to use MMA, you may e.g. solve for d as a function of the variables a,b,c (assuming you want real solutions):

eq = 811 a + 741 b + 1025 c + 752 d == 94508.16372;
Solve[eq, {d}, Reals]
(* {{d -> 125.676 - 1.07846 a - 0.985372 b - 1.36303 c}} *)


Or you may e.g. use Reduce to solve for a as a function of the variables b,c,d

Reduce[eq, {a}, Reals]
(* a == 116.533 - 0.913687 b - 1.26387 c - 0.92725 d *)

• Thanks Daniel. But what I want is to find the numerical solutions for all the variables. Is that possible?
– YzWu
Commented Jan 22, 2021 at 17:15
• There is an infinity of solutions, parametrized by 3 variables. If you want one unique solution, you must specify 3 more equations to pick out the one you want Commented Jan 22, 2021 at 19:37