how do you solve for x?

(1/x) + X = 4

Question

how do you solve for x?

(1/x) + X = 4

anonymous · Answer

multiply everything by x

amistre64 · Answer

which x?

anonymous · Answer

both, meant to lower case the second one

amistre64 · Answer

:)

amistre64 · Answer

adrians got it good then :)

anonymous · Answer

1+x^2=4x, x^2-4x+1=0,

anonymous · Answer

that isnt right though? because you cant factor $$x^2 - 4x + 1$$

amistre64 · Answer

its quadratic; so there could be at most 2 answers

anonymous · Answer

don't factor. Solve

anonymous · Answer

well how would you solve it from there?

anonymous · Answer

solutions= -b plus or minus sqrt(b^2-4ac) everything divided by 2a. where a,b and c the coefficients

amistre64 · Answer

$$\frac{1}{x} + x = 4$$
$$\frac{1}{4x} + \frac{x}{4} = 1$$
$$\frac{1}{4x} + \frac{x^2}{4x} = \frac{4x}{4x}$$
$$1+x^2 = 4x$$
$$x^2-4x+1 = 0$$
$$x^2-4x+(4-4)+1 = 0$$
$$(x-2)^2-3 = 0$$
$$(x-2)^2 = 3$$

amistre64 · Answer

can you solve it from there?

anonymous · Answer

how did you go from 1/4x + x/4x = 1/4 to 1/4x + x^2/4x^2 = x/4x?

amistre64 · Answer

algebra; its was more work but same conclusion as adrians tho

anonymous · Answer

because if you multiplied both sides by x/x then you would get x/4x^x not 1/4x

amistre64 · Answer

you dont have to multiply both sides by "1", thats just a trick used to change form and retain the same value

amistre64 · Answer

x/x =1 so it is benign in the process

anonymous · Answer

no what im saying is when you go from the second to the third step in your explination how did you just add an x to the second segment and the right side but not to the first part on the left side?

amistre64 · Answer

i was getting like denominators; 4x and 4, i need an x to match; so x/x changes the way it looks without changing the value

anonymous · Answer

oohhh i understand now

amistre64 · Answer

the right side was 1/1; so i just modified it to 4x/4x

amistre64 · Answer

:)

anonymous · Answer

then how did you take out the 4x on bottom?

anonymous · Answer

too much trouble for a trivial matter. u should multiply and avoid fractions

amistre64 · Answer

when you have the same denominators all the way across; the only thing that matters is the tops; you could just as well say that I multiplied all of it by 4x

amistre64 · Answer

id have done it adrians way as well; but i like to show that there is more than one way to structure an answer and to use what you feel most comfortable with

anonymous · Answer

alright well thanks i think i understand now :D

amistre64 · Answer

dont be afraid to play around with it and see where it takes you :)

anonymous · Answer

haha alright thanks!