Question

SOLVING FOR QUADRATIC EQUATIONS!
If I solve it in different ways, should I be gettingthe same answer?
Say the equation is x^2 + 6x + 17 = 0
if i used the Quadratic Formula and "Complete the Square", should it be the same?

Answer 1

@precal

Answer 2

@campbell_st
please?

Answer 3

ok... so lets solve it

using the general quadratic formula

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

a = 1, b = 6 and c = 17

so \[x =\frac{ -6 \pm \sqrt{36 - 68}}{2}\]


this will be simplified to

\[x = \frac{-6 \pm \sqrt{- 30}}{2}\]

Answer 4

I hope that makes sense.. and the curve is positive definite... and will have complex roots

Answer 5

yes, i solved it and for -3 plus or minus 2 square root 2

Answer 6

oops made a calculation error

\[x = \frac{-6\pm \sqrt{-32}}{2} \]

this can be simplified

\[x = \frac{-6 \pm 4i \sqrt{2}}{2}\]

\[x = -3 \pm 2i \sqrt{2}\]

Answer 7

WAIT!
Can i change the problem??
My main question is would doing it 2 different ways be the same answer. for that problem it worked, but it didn't for another.
i didn't know if i did it wrong, or if it doesn't work with all problems

Answer 8

yes it is the same answer... as any quadratic will only have 2 solutions

here is an easy example

x^2 +8x + 7 = 0

factorising (x + 7)(x + 1) so x = -7, -1

completing the square
x^2 + 6x = -7

x^2 + 8x + 16 = - 7 + 16

(x + 4)^2 = 9

\[x + 4 = \pm 3\]

so x = -4 - 3 and x = -4 + 3 therefore x = -7, -1

Answer 9

oops should be 8x... when completing the square

Answer 10

I understand still :)
ummm. what if on another problem i did the quadratic equation and got something with a square root, but did complete the square and got 1..
I totally messed up somewhere?

Answer 11

x^2-2x-1=0

Answer 12

well its a simple arithmetic mistake... I'd expect..

whats the question..?

so completing the square you would have

\[(x - 1)^2 = 1 + 1\]

then \[x = 1 \pm \sqrt{2}\]

Answer 13

by GQF you would get

\[x = \frac{ -2 \pm \sqrt{ 4 - 4 \times 1 \times -1}}{2}\]

so \[x = \frac{ -2 \pm \sqrt{8}}{2} \]

which will simplify to the answer for complete the square

Answer 14

oops should be 2 not -2

Answer 15

OHHHHHHkay.
I think i get it.
so even if they look like different numbers, they would solve to the same thing if simplified and everything?

Answer 16

Thank you so much :]

Answer 17

yes... its the simplification process... if I simplify the GQF version I get

\[x = \frac{2 \pm 2\sqrt{2}}{2}\]

cancel the common factor of 2 and you get

\[x = 1 \pm \sqrt{2}\]

Answer 18

yes campbell_st is correct
both methods should produce the same result
for example if you factor the quadratic (assume you can factor it) and if you use the quadratic formula, you should get the same solutions
also if you complete the square and use the quadratic formula, you should get the same solution
if you do not, then you probably made a small mistake somewhere
you will find that one method is sometimes faster than the other
personally
I always factor if possible
and if I can not factor I use the qudratic formula
I rarely ever complete the square unless I am told to do so