SOLUTION: how do i solve this x+12/x=7

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Question 394489: how do i solve this x+12/x=7
Found 2 solutions by richard1234, MathLover1:
Answer by richard1234(7193) (Show Source):
You can put this solution on YOUR website!
I have changed the topic, since the question is not linear algebra (linear algebra studies vectors, vector spaces, and matrices).

Anyway, we have . Multiplying through by x,

This factors pretty nicely:

--> x = 3, 4

Answer by MathLover1(20850) (Show Source):
You can put this solution on YOUR website!

...both sides multiply by

...add to both sides

...use quadratic formula

Solved by pluggable solver: Quadratic Formula

Let's use the quadratic formula to solve for x:

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=1, b=-7, and c=12

Negate -7 to get 7

Square -7 to get 49 (note: remember when you square -7, you must square the negative as well. This is because .)

Multiply to get

Combine like terms in the radicand (everything under the square root)

Simplify the square root (note: If you need help with simplifying the square root, check out this solver)

Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

or

Lets look at the first part:

Add the terms in the numerator

Divide

So one answer is

Now lets look at the second part:

Subtract the terms in the numerator

Divide

So another answer is

So our solutions are:

or