# Doing arithmetic in one step

Let's say you have

$0.5\times 1.5 \ x^2 - (0.5\times 3.2 \times 1.5) = 23$

or something similar. Is there an easy way to just get $x^2$ in one step?

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And I mean equations like this in general. where you have a whole lot of numbers, and just one variable, and you want just one step to get it. It takes up a lot of time on physics/mathematics tests to perform these operations in more steps than necessary. –  JohnPhteven Nov 5 '12 at 16:04
What do you call 'one step'? One sentence can contain more subsentences, for example. For a one step solution: Add the constant term seen on the right of LHS to the equation, then divide it by the coefficient of $x^2$. –  Berci Nov 5 '12 at 16:10
Why has this question got an up-vote? –  Epictetus Nov 5 '12 at 16:24
@Epictetus Someone can probably relate with me, it's not the best question, but I'm not asking it on mathoverflow or something similair, here questions like this one are allowed.. –  JohnPhteven Nov 5 '12 at 16:43
@ZafarS I don't think I'm the only one that is surprised by the up-vote on this question. I am also surprised at your swift defense of it. The question is elementary (even by the standard of the other questions you have asked in the past), does not show any useful research and there is no attempt at the answer. An up-vote in this case (I'm sorry to say) just doesn't appear to be warranted. –  Epictetus Nov 5 '12 at 17:42

If $a \times x^2 - b = c$ then $$x^2 = {c+b\over a}$$ There is really no easier way to find $x^2$ than just computing the value of this expression. In your case, $a = 0.5\times 1.5=0.75$, $b=0.5\times 3.2\times 1.5=2.4$, and $c=23$.
Sometimes you can save time by cancelling common factors first, but that is not the case here, since $c=23$ has no nice factor in common with $b$.
One moves expressions around in his head. Performing mental gymnastics, we have $x^2=\frac{23+0.5\times 3.2\times 1.5}{0.5\times 1.5}$.