Question

G(x) = x^2 + 6x + 1

Find the solutions of g(x). Show each step

Answer 1

g(x) = x2 +6x + 1
-1 -1
-1 = x^2 + 6x 6/2 = 3 ^2 = 9
+9 +9
8 = (x+3) ^2
-8 -8
It's Here that i don't understand the square root part.

Answer 2

@MDoodler ?

Answer 3

Use the quadratic formula on x^2 + 6x + 1

\(x = \frac{ - b \sqrt {b^2 - 4ac}}{2a} \)

Answer 4

\(x = \frac{ -6 \sqrt {6^2 - 4a(1)(1)}}{2a} \)

Answer 5

:/ huh?

Answer 6

Ok, you have not used the quadratic formula yet in class?

Answer 7

I never understood it so i use another way. the one above.

Answer 8

Your solutions are going to be roots so it is best to use the quadratic formula

Answer 9

square roots that is

Answer 10

could you show me how to use it?

Answer 11

Yes, sorry my computer went out.

Answer 12

From here 8 = (x+3)^2, which you already have, we need to square both sides

\( 8 = (x+3) ^2\)
Square both sides

\( \sqrt{ 8} = \sqrt{(x+3) ^2}\)
\( \sqrt{ 8} = x+3\)
\( \sqrt{ 8} \)
\( \sqrt{ 8}\)
We squared the right side now lets square the left side

To square the left side, we need to simplify the square
\( \sqrt{ 8}\)
\( \sqrt{ 4} \sqrt{2} \)
\( 2 \sqrt{2} \)
Now we have
\( 2 \sqrt{2} = x+ 3\)
\( -3 + 2 \sqrt{2} = x+ 3 + -3\)
\( -3 + 2 \sqrt{2} = x\)


So your solutions are
\( x = -3 + 2 \sqrt{2} \)

\( x = 2 \sqrt{2} -3 \)

I can also show you the quadratic formula way too, which I think is easier

Answer 13

Sure, can you show the easier way. But I do understand this method.

Answer 14

Thank you so much ^_^