Solving EquationsDate: 9/3/95 at 7:28:20 From: "S. Capodici" Subject: Formulas Can you help? If n=x^2+y then how can you work out x if you know n and y, and work out y knowing n and x.? Is there an easy to read book on rearranging formulas? Thanks, M.C. Date: 9/4/95 at 14:31:7 From: Doctor Ethan Subject: Re: Formulas Hey M.C. I guess I don't know of an easy to read book, but I can give you a few tips to get you started. Two things you need to realize and remember are: 1. If you add or multiply the same thing to both sides of an equality, it is still an equality. For instance. If 3 + b = w then 15 + 3+ b = w + 15. Similarly If 3+ b = w then 17(3+b) = 17 * w. 2. If you take the square root of both sides of an equation, then they are both equal in magnitude (the sign could be different). For example: If x^2 = 4 then x = 2, or -2 and if 3 + r = y^2 then the square root of (3+r) equals y or -y. From here on I will use Sqrt(3+r) to mean the square root of (3+r). These two facts are all we need to solve the problems that you asked. For n = x^2 + y, when we want to solve for x: First we will use rule number 1 to get the x by itself. We will do this by adding -y to both sides. We then have n - y = x^2 y-y but y-y =0 so that reduces to n - y = x^2. Now we can use rule 2 and get: Sqrt(n-y) = x or -x. Similarly if we want to solve for y: First we add -x^2 to both sides, and then we have n - x^2 = x^2 +y - x^2 which reduces to n - x^2 =y So that is it. I hope that this has helped some. -Doctor Ethan, The Geometry Forum |
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