I cannot understand how quadratic formula to solve for $x$ was derived.

On this website, it explains the steps

Following I understand

enter image description here

but I cannot understand how they got


and why they are squaring it


Really, I am baffled!


marked as duplicate by Davide Giraudo, user228113, Mark Bennet, YoTengoUnLCD, user147263 Dec 23 '15 at 19:51

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  • 2
    $\begingroup$ to complete the square $(x+\frac{b}{2a})^2$ $\endgroup$ – janmarqz Dec 23 '15 at 17:30


This is the completing the square trick. Usefull in many other cases and simple to visualize.

enter image description here

The black square is $x^2$, the red rectangle is $bx$, so $x^2+bx$ can be transformed to a square adding the little blue square, that is $(b/2)^2$.

  • $\begingroup$ Honest to God, the concept still has to soak in. A picture is worth 1000 words. $\endgroup$ – Rhonda Dec 24 '15 at 16:10





Then we know that



This process is called completing the square. Now we can factor a perfect square. Is this answer sufficient?


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