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November 21st, 2014, 11:34 AM   #1
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Fractions! With powers! Or equations with powers and a number

I have knowledge of solving fractions without powers, e.g. (2x+2)/3+x/5=10.
But for (2x(x+1))/2=20, I got to 2x^2+2x=40, what do I do next?
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November 21st, 2014, 12:51 PM   #2
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Quote:
Originally Posted by alifeee View Post
I got to 2x^2+2x=40, what do I do next?
That's a classical second degree equation.

$\displaystyle
\begin{aligned}
& 2x^2 + 2x -40 = 0 \\
& x^2 + x - 20 = 0 \Rightarrow ax^2 + bx + c \\
& x = {-b \pm \sqrt{b^2 - 4ac} \over 2a} \\
\end{aligned}
$


You can continue..
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November 21st, 2014, 01:24 PM   #3
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$\displaystyle x^2+x-20=(x+5)(x-4)$
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November 21st, 2014, 04:47 PM   #4
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Quote:
Originally Posted by alifeee View Post
But for (2x(x+1))/2=20, I got to 2x^2+2x=40, what do I do next?
$\displaystyle \color{blue}{\dfrac{\not{2}x(x+1)}{\not{2}}=20\ \Longleftrightarrow\ x(x+1)=20
\\\;\\ \\\;\\
x\ \ and\ \ x+1\ \ can\ be,\ here,\ two\ consecutive\ integers.
\\\;\\
4\cdot5 = 20
\\\;\\
(-5)\cdot(-4)=20}$
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