Solve and show and explain work x^2 + bx + c = 0

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Solve and show and explain work x^2 + bx + c = 0

Mathematics
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Try applying the quadratic equation to this one.
\[x = \frac{ -b \pm \sqrt{b^{2} - 4ac} }{ 2a }\]

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Other answers:

@BubbaMurphy Do you have a different way to do this problem???
LogicApple's way is definitely the way to do it.
in this case, a=1
Is that really how yo would solve it
would A, B, and C = 1
Based on the equation you supplied, a = 1, b = b, and c = c.
They are coefficients of whatever quadratic you are talking about. Did you have a quadratic in mind?
what you mean
\[6x^{2} - 9x + 12 = 0\] \[-5x^{2} + x - 10 = 0\] \[x^2 + x - 1 = 0\] These are some examples of quadratics, all set equal to 0.
Yea I know that
Oh, ok... so what is your question?
We have to solve x^2 + bx + c = 0 for bonus and I have no idea what to do
I suggested using the quadratic equation. The only difference between x^2 + bx + c = 0 and the quadratics that I mentioned is that the coefficients in your equation are only known by their variable letter. But that is ok, you can still apply the quadratic formula to them. The solutions to x^2 + bx + c = 0 is: \[\frac{ -b \pm \sqrt{b^{2} - 4c} }{ 2 }\] This is the same thing I wrote before, except I let a = 1 because the coefficient of x^2 in your equation is 1.
We didn't learn that equation you gave me
What about completing the square ?
so is that the answer
Yes, but you would arrive at the same answer if you complete the square. Both techniques are valid for solving quadratic equations.
I have to show my work, so how would I show it
Well if you're using the quadratic equation you could say "applying the quadratic equation". But if you wanted to complete the square then: |dw:1359081924838:dw|
I think you can use sum and product of roots: \[\alpha +\beta= \frac{ -b }{ a }\] \[\alpha \beta=\frac{ c }{ a }\]
b^2/4
1 Attachment
|dw:1359082578453:dw|
(b/2)^2 = b^2/4
After (x + b/2)^2 = b^2/4 - c. Find the square root of both.
Yes
I got x + b/2 = b/4 - c. Is that correct?
no the square root of both sides gives: x + b/2 = ± sqrt(b^2/4 - c)
what then
All the steps are in the picture attached.
1 Attachment
I am sorry the last step in attachment is the answer
Oh ok did you get it figured out ?
so x = +/- sqrt b^2 - 4c /2 is the answer
|dw:1359083804186:dw| yes
Will you forgive me @LogicalApple ?
What for? It's a learning experience
I probably annoyed you a lot

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