Where should the values be placed to correctly solve for x?

  • MHB
  • Thread starter 06Rousher
  • Start date
In summary, the conversation discusses solving the equation x=2+1/x through various methods. The main method proposed is to multiply both sides by x and solve the quadratic equation. The final solution is x = 1 +/- sqrt(2). The conversation also mentions the general formula for solving quadratic equations.
  • #1
06Rousher
9
0
"x=2+1/x"

What I got is this: -x^2=2 then x^2=-2, then x=4
 
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  • #2
Re: Wanting to make I got this correct

x = 2 + 1/x

To find x, I think it would be appropriate to multiply both sides with x, and solve the quadratic equation.
 
Last edited:
  • #3
Re: Wanting to make I got this correct

lfdahl said:
x = 2 + 1/x

To find x, I think it would be appropriate to multiply both sides with x, and solve the quadratic equation

So x^2-2x-1? Doesn't seem like that would be solvable.

I got 2.41 for x
 
  • #4
Re: Wanting to make I got this correct

Why not? You did solve the equation:

x^2-2x-1 = 0 --> x = 1+/- sqrt(2)
 
  • #5
Re: Wanting to make I got this correct

lfdahl said:
Why not? You did solve the equation:

x^2-2x-1 = 0 --> x = 1+/- sqrt(2)

How did you get to x=1 +/- sqrt(2)?
 
  • #6
Re: Wanting to make I got this correct

The quadratic equation: x2- 2x - 1 = 0

Discriminant: D = (-2)2-4(1)(-1) = 8

The two solutions:

x1 = (2 + sqrt(8))/2 and x2 = (2 - sqrt(8))/2

or

x1 = 1 + sqrt(2) and x2 = 1 - sqrt(2)

In general for solving a quadratic equation:

\[ax^{2}+bx+c=0 \\\\D = b^{2}-4ac \\\\x = \frac{-b\pm \sqrt{D}}{2a}\]
 
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  • #7
Re: Wanting to make I got this correct

Thank you so much

That last part really helped me understand it, I was having trouble on where to place the values
 

FAQ: Where should the values be placed to correctly solve for x?

How do I solve an equation for x?

To solve an equation for x, you need to isolate the variable on one side of the equation and perform the inverse operation on the other side. This will give you the value of x that makes the equation true.

What is the first step in solving an equation for x?

The first step in solving an equation for x is to simplify both sides of the equation by combining like terms and using the distributive property if necessary. This will make it easier to isolate the variable.

Can I solve an equation for x without using algebra?

Yes, there are other methods for solving equations for x, such as graphing or using a calculator. However, algebra is the most commonly used method and is essential for understanding the principles behind solving equations.

What do I do if I get a negative value for x?

If you get a negative value for x, it means that the equation has no real solution. This can happen when taking the square root of a negative number or when dividing by a negative number. In this case, you can state that there is no solution for x.

Can I check my solution for x?

Yes, it is always recommended to check your solution for x by substituting the value back into the original equation and making sure it satisfies the equation. This can help catch any mistakes made during the solving process.

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