How do you solve #x^2+6x+2 = 0# ?
2 Answers
Explanation:
Solving this by factoring is very difficult because this polynomial doesn't factor super easily.
If you use graphing, you can see the zeros (also called roots) of the euqation that touch the
graph{x^2+6x+2[-6,1,-8,4]}
However, using the interactive graph, you can see the zeros are not "nice" or "neat", but are rather longer decimal answers.
Next, is completing the square. Here is how you complete the square:
1) Start with the original equation
Recall that
2) Take the
3) Add and subtract this new value, 9, to the equation
Rearranging with parenthesis, we get
The part inside the parenthesis is a perfect square
4) Factor the part inside the parenthesis
5) Finally, solve for
This final answer are the two roots you saw in the graph above:
See below for two of the ways mentioned (I didn't understand if factoring meant some way of taking common factors, or using the quadratic formula).
Explanation:
To use a graph to your advantage, you'll need to have it presented to you, such as with a graphing calculator, as you can't really draw it without knowing the solutions to the equations already. Unless you approximate it using calculus, which is probably not the point here. So let's graph
graph{x^2+6x+2 [-10, 10, -5, 5]}
it's not visible here, but the points at which the graph intersects the
Now for completing the square. There's an identity that tells us that
We need to convert the left part of our equation to be of the form seen on the left of the equality above. So, let's add
And now we have
the two solutions.
