Solving the algebraic equation

Question

I am trying to solve this: $$x-40={-400\over x}$$ The answer must be $x=20$
Please give step by step explanation.

Answer 1

Assuming $x\neq 0$, multiply both sides of the equation by $x$ to get: $$x\cdot(x-40) =-400$$ Next expand the left hand side and re-arrange to get: $$x^2-40x+400=0$$. To factor the left hand side, look for two numbers that when you multiply you get 400 and add to -40. Doing that yields $$(x-20)(x-20) =0.$$ You should be able to take it from here.

Answer 2

Step 1. Multiply through by x.

Step 2. Move everything to one side.

Step 3. Use the quadratic formula.

Step 4. Conclude that $x=20$.

Answer 3

Simplifying the equation gives :

$ x^2 - 40x + 400 = 0$

$ => {(x-20)}^2 = 0 $

$=> x = 20 $