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$\sqrt{\frac{x}{-4.9}} - \frac{x}{340} = 4.68$

The following is my work so far:

$\sqrt{\frac{x}{-4.9}} = 4.68 + \frac{x}{340}$ $\frac{x}{-4.9} = 21.9 + \frac{x^2}{115600} + \frac{3182.4x}{115600}$ $x^2 + 26774.2x + 2531640 = 0$

Using the quadratic formula, I get:

$x_1 = -94.9$ $x_2 = -26679.3$

However, the answer in my book only mentions $-94.9$. I checked a couple of online equation solvers also they only mention -94.9. Additionally, plugging in -26679.3 into the original equation does not work - however plugging it into the derived quadratic does. This must mean my derived quadratic equation is incorrect - does anyone have any idea why?

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    Is because some of your steps (one actually) is not necessarily reversible. When you have an Equation, lets call it EQ1, and you square it to get EQ2, any solution to your initial equation is also a solution to EQ2. But some solutions to EQ2 could actually come from squaring something like $(-2)=2$. Your particular $x$ can lead to a LHS of $-2$, and a RHS of $2$, so is not a solution to your equation, but becomes a solution after you square both sides...2012-09-30

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It's because when you squared both sides of your equation, you made the "negative square root" into a possible solution, whereas $\sqrt{}$ always means the positive square root.

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    Ah, that makes much more sense. Thank you for your help.2012-09-30