Question

Using complete sentences, explain how you would use the quadratic formula to solve x2 + 7x = –3. Why is the quadratic formula the best method to use?

Answer 1

well first to use the quadratic formula we need ax^2+bx+c=0.
so we need to add 3 on both sides such that we have x^2+7x+3=0.
now using the quadratic equation, we know a=1, b=7, and c=3.
now we just plug those numbers into the quadratic formula which is:
\[x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}\].
Wherever you see an a, you will put 1.
Wherever you see a b, you will put 7.
Wherever you see a c, you will put 3.
So we have
\[x=\frac{-7-\sqrt{7^2-4(1)(3)}}{2(1)}\].
Then I would simply using order of operations.
First thing to do evaluate whats in the square root( this is our grouping symbol).
The operations tells us to to evaluate the exponent, 7^2=49.
Then perform the multiplication as it occurs left from right inside. 4(1)(3)=4(3)=12.
Now we do the subtraction inside, we have 49-12=37.
so this is what we have now:
\[x=\frac{-7 \pm \sqrt{37}}{2(1)}\]
so now we can perform the operation on bottom, 2(1)=2.
So we have
\[x=\frac{-7 \pm \sqrt{37}}{2}\].
This saids we have solutions and they look like
\[x=\frac{-7+\sqrt{37}}{2},\frac{7+\sqrt{37}}{2}.\]

Answer 2

this saids we have two solutions*