# Make 'b' the subject in the quadratic formula [closed]

Solve for b in terms of a,x and c in the fastest way possible.

## closed as off-topic by JonMark Perry, Glorfindel, SteveV, rhsquared, Deusovi♦Jan 7 at 21:52

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• "This question is off-topic as it appears to be a mathematics problem, as opposed to a mathematical puzzle. For more info, see "Are math-textbook-style problems on topic?" on meta." – JonMark Perry, Glorfindel, SteveV, rhsquared, Deusovi
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• "subject" is a somewhat vague term. What you're presumably asking for is known in math as "isolating" or "solving for". "fastest" is also ambiguous. Do you mean "fewest operations"? – Acccumulation Jan 7 at 20:43

From the quadratic equation

we can go back to the original equation $$ax^2 + bx + c = 0$$ and solve it for $$b$$, which yields: $$b = - \frac{ax^2 + c}{x}$$

• Wow, I know mathematics university graduates who couldn't crack that one out. I love this exchange. Speaking of which. How do the tickings work for people giving out questions with both 1 answer, and an answer the OP knows? – yolo Jan 7 at 20:33
• If you know an even faster way, then wait some time, so that people have a chance to come up with it on their own. – A. P. Jan 7 at 20:34
• And since this is the fastest way I know of? – yolo Jan 7 at 20:35
• @yolo Then you may tick it as soon as you want. But I fear that this question is not 'puzzling' enough and might get closed. But you could also wait whether someone comes up with a more puzzling-like solution. – A. P. Jan 7 at 20:37
• A.P I think the firsy sentence in your answer is a bit of a giveaway... – yolo Jan 7 at 20:48

Not the fastest... I kind of assumed we had to pretend we didn't already know the answer.

Multiply by 2a

$$2ax=-b \pm \sqrt{b^2-4ac}$$

Square everything

$$2ax*2ax=b^2+b^2-4ac \pm 2b\sqrt{b^2-4ac}$$

Simplify

$$4a^2x^2=-4ac-2b(-b\pm\sqrt{b^2-4ac})$$

Hey that looks familiar

$$4a^2x^2=-4ac-4bax$$

Finish it up

$$b=-\frac{ax^2+c}{x}$$

• 'we had to pretend we didn't already know the answer'- how so? I've never known anyone who knows the formula for b as general knowledge. – yolo Jan 7 at 20:46
• ax^2+bx+c=0 is common knowledge and pretty much is solved. That answer is correct; i think this adds to the discussion but is not fast enough. – kaine Jan 7 at 20:56