# When to complete the square?

So i just have a general knowledge question. not rly hw related

say u have a quadratic function or equation 4x2 – 2x – 5. Why would u have to complete the square in this situation? i know how to complete the square perfectly fine, but this was just bugging me.

I know that if ur graphing u complete the square to get it in the form a(x-h)^2 +c which makes it easier to visualize, but in the case of a quadratic equation i dont see why u can't just make everything equal to x as is.

## The Attempt at a Solution

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symbolipoint
Homework Helper
Gold Member
One completes the square to enable easy manual graphing and to help identify center, vertex, and other features of the graph.

Mentallic
Homework Helper
Completing the square will also be used in maths later on with graphing circles, integration, inequality proofs etc.

Also, completing the square makes graphing a quadratic easier when there are no real roots.
If we solve $$x^2+2x+2=0$$ then the roots are $$x=-1\pm i$$ which doesn't really tell us anything about graphing it (other than it's completely above/below the x-axis), while $$(x+1)^2+1$$ is much clearer.

verty
Homework Helper
Completing the square can be safer if you practice it, and it is good algebra practice to do it that way, if you have the time.

vela
Staff Emeritus
Homework Helper
So i just have a general knowledge question. not rly hw related

say u have a quadratic function or equation 4x2 – 2x – 5. Why would u have to complete the square in this situation? i know how to complete the square perfectly fine, but this was just bugging me.

I know that if ur graphing u complete the square to get it in the form a(x-h)^2 +c which makes it easier to visualize, but in the case of a quadratic equation i dont see why u can't just make everything equal to x as is.
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oops Sorry about that. Also thanks for those who replied. I pretty much get it now.
Thanks for the help.