Question

how to solve quadritic formala then simplify?
x^2+8x+14=0

Answer 1

So you need to figure out:

1) what 2 numbers multiply to make 14
AND
2) do those 2 numbers ALSO add to make 8?

Answer 2

so i write as quadritic formula right?

Answer 3

do you already know the formula?

Answer 4

@johnweldon1993 not solved by factoring hence required to use the formula

Answer 5

yes i do but then its wrong cause they wan me to simplify

Answer 6

You can via grouping as I did,

however, since you (the poster) brought up the quadratic formula, absolutely we can do that

\[\large \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\]

Answer 7

What is 'a' 'b' and 'c' in this equation?

Answer 8

1,8,14

Answer 9

Great, so we have

\[\large \frac{-8 \pm \sqrt{8^2 - 4(1)(14)}}{2(1)}\]

The painful part is the simplification

\[\large \frac{-8 \pm \sqrt{64 - 56}}{2}\]

what does THAT simplify to?

Answer 10

-8+8/2

Answer 11

Not quite, you lost the square root

\[\large \frac{-8 \pm \sqrt{8}}{2}\]

now, we can simplify that further right? what if I wrote this like

\[\large \frac{-8 \pm \sqrt{4\times 2}}{2}\]

what could we do?

Answer 12

divide the 8 by 2?

Answer 13

Not quite, was mainly talking about the square root part

Hint* what is the square root of 4?

Answer 14

2

Answer 15

Right

so we can change

\[\large \frac{-8 \pm \sqrt{4\times 2}}{2}\]
to
\[\large \frac{-8 \pm 2\sqrt{ 2}}{2}\]

NOW we can divide everything by 2

\[\large \frac{\cancel{-8}\rightarrow -4 \pm \cancel{2}\sqrt{2}}{\cancel{2}}\]

written more nicely

\[\large -4 \pm \sqrt{2}\]

Answer 16

Make sense?

Answer 17

yes but could i just divide the numbers first before solving?

Answer 18

What do you mean? Like before I simplified the square root?

Answer 19

like 8 could be divided to 4 before writing out the problem

Answer 20

You COULD have, but the 2 would still be in the denominator for the 2nd part of the numerator...see what I mean

\[\large \frac{-8 \pm \sqrt{8}}{2}\]

\[\large -4 \pm \frac{\sqrt{8}}{2}\]

Answer 21

That's why I wanted to simplify that square root first....making it 4 times 2...and then bringing the 2 out in front made it so THOSE 2's would cancel and we wouldnt need to deal with that annoying fraction

Answer 22

yah so that wont work and isthe anser plus or minus?

Answer 23

Not quite,

Whenever you see a solution with a +/- sign, it means you have 2 equations

Here we have

\[\large -4 \pm \sqrt{2}\]

whih will break into

\[\large -4 + \sqrt{2}\]
and
\[\large -4 - \sqrt{2}\]

Answer 24

ok thanks i really got to practice its on a final

Answer 25

No problem, yeah the quadratic formula can help out a lot in these cases if you're not familiar with grouping or completing the square etc...

Answer 26

oh yah i really struggling with factoring trinomials etc