Solving for x w/polynomial.

[jonboy]

Can someone please tell me what I am doing wrong here? I arrive at a negative sqrt which is not supposed to happen.

\(\displaystyle \L \;\frac{1}{x-8}+\frac{3}{1}=\frac{x}{x-8}\)


Get like denominators: \(\displaystyle \L \;\frac{1}{x-8} + \frac{3x-8}{x-8} = \frac{x}{x-8}\)


Simplify: \(\displaystyle \L \;\frac{3x-7}{x-8}=\frac{x}{x-8}\)


Cross Products: \(\displaystyle \L \;x^2-8x=3x^2+56\)


Simplify: \(\displaystyle \L \;2x^2+8x+56=0\)


Quadratic Formula: \(\displaystyle x = \frac{{8 \pm \sqrt {( - 8)^2 - 4(2)(56)} }}{{2a}}\,\to\,x = \frac{{8 \pm \sqrt { - 384} }}{4}\)


Huh? I did everything right how did I get a negative sqrt on my Quadratic?

 

[skeeter]

Can someone please tell me what I am doing wrong here? I arrive at a negative sqrt which is not supposed to happen.

\(\displaystyle \L \;\frac{1}{x-8}+\frac{3}{1}=\frac{x}{x-8}\)



Get like denominators: \(\displaystyle \L \;\frac{1}{x-8} + \frac{3x-8}{x-8} = \frac{x}{x-8}\)
2nd fraction on the left side ... 3(x-8)/(x-8) = (3x-24)/(x-8)


Simplify: \(\displaystyle \L \;\frac{3x-7}{x-8}=\frac{x}{x-8}\)


Cross Products: \(\displaystyle \L \;x^2-8x=3x^2+56\)


Simplify: \(\displaystyle \L \;2x^2+8x+56=0\)


Quadratic Formula: \(\displaystyle x = \frac{{8 \pm \sqrt {( - 8)^2 - 4(2)(56)} }}{{2a}}\,\to\,x = \frac{{8 \pm \sqrt { - 384} }}{4}\)


Huh? I did everything right how did I get a negative sqrt on my Quadratic?

 

[stapel]

I'm pretty sure that 3(x - 8) does not equal 3x - 8.

Also, since you have an equation, why not just clear the denominators? Multiply through by the common denominator, and then solve the resulting linear equation:

. . . . .1 + 3(x - 8) = x

Or just plug the various given values into the equation, until you find the one that works.

Eliz.

 

[galactus]

You don't need quadratics, jonboy.

\(\displaystyle \sout{(x-8)}\frac{1}{\sout{x-8}}+(x-8)3=\sout{x-8}\frac{x}{\sout{x-8}}\)

\(\displaystyle 1+3x-24=x\)

\(\displaystyle x=\frac{23}{2}\)

 

[jonboy]

Oooh ok. Yeah who needs Quadratic anyways. :wink: Thank you Skeeter, Stapel and Galactus.

 

[Denis]

Another way for your repertoire, Jonboy; move the 1 / (x-8):
x / (x-8) - 1 / (x-8) = 3
(x - 1) / (x - 8) = 3
crisscross multiply and you're almost done :idea: