Question

the answer to the original equation (generated at math.com) is
x= 11 and x=7.

the original equation is : x^2 -18x +77 =0

my attempt at the quadratic formula produced : x=(18 ± 2√(61) / 2)

i decided i had done something incorrectly and started completing the square from the original equation.

to avoid a negative square root, how can i use the square root property on this ?
(x+81)^2 = -158
or am i missing something about the rules of negative numbers and square roots ? I thought negative square roots were not allowed. thanks :)

Answer 1

it is clear that $$x^2-18x+77=(x-11)(x-7)$$ so you can find the answer straight away.

Answer 2

how is that clear ?

Answer 3

i am attempting to learn how to use the quadratic formula or "completing the square" method because i have a test for a job in less then a month and these two choices gain an answer 100% of the various problems encountered.

Answer 4

havent you done factorization of binomials. Normally it can be done by mind. It is same as the method that you tried. But you've made some small mistakes in squaring

$$x^2-18x+77=x^2-2(9)x+9^2 -9^2+77=(x-9)^2-81+77=(x-9^2)-4\\
=(x-9)-2^2=(x-9-2)(x-9+2)=(x-11)(x-7)$$

there is a method of doing this by just thinking (only if you get simple factors)

Answer 5

thanks BAdhi, i am looking it over. i have read about factoring polynomials once and abandoned it due to it's lack of success in solving all quadratic equations.

Answer 6

well sorry to interrupt. let me give u a brief explanation on factoring using completion of square method.
\(x^2-18x+77=0\)
divide the coefficient of the middle term by 2.
The coefficient of the middle term is -18. when u divide by 2 u get -9.
Find the square of it . u will get 81.
nw u need to add 4 to make 77 as 81. if u add 4 to one side of the equation u have to add 4 on the other side in order to make both sides equal.
\(x^2-18x+77+4=4\)
\(x^2-18x+81=4\)
\((x-9)^2=2^2\)
\(x-9=\pm2\)
\(x-9=2~or~x-9=-2\)
\(x=11~or~x=7\)
Does that help? @ibew

Answer 7

ok, i see where i did not take the square root of 81 and make it 9 for (x-9)^2
and it seems that moving the 77 to the other side was not necessary. the instructions from a collage book i have as one of my resources shows it as the first task.

i also see that you evaded √4 by converting it to 2^2. though it would have worked out to 2 any way.

yes, this helps me know that this collage math book has errors that cause me great trouble :( thanks for clearing this up for me :)

Answer 8

welcome:)

Answer 9

well r u clear with quadratic formula usage?

Answer 10

no, actually. the same equation resulted in : x=(18 ± 2√(61) / 2) : using the quadratic formula . if you would like to assist my in learning what i have done incorrectly, it would be equally appreciated.

i know the quadratic formula as:

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

Answer 11

well can u tell me what are the values of a,b and c from equation?

Answer 12

*ur

Answer 13

\[a x^{2} + b ^{2} + c = 0 \]

there for , in the quadratic equation : x^2 -18x +77 =0

a=1 , b=18 , and c=77

Answer 14

oops. ax^2 + bx + c = 0

Answer 15

i am new at using the equation editor :D

Answer 16

that's k:) well ur b=-18

Answer 17

oh yeah, thanks

Answer 18

maybe it will giv u the correct answer this time

Answer 19

i used -18 last time. it was a typing error this time around.

Answer 20

i will run it through again ... be back

Answer 21

ha k:)

Answer 22

x^2 -18x +77 =0

a=1 b=-18 c=77

x= -(-18)± √(-18^2 - 4*1*77)
------------------------
2


x= -(-18)± √(-18^2 - 3388)
------------------------
2


x= -(-18)± √(-18^2 - 1694^2)
------------------------
2

x= -(-18)± -18^2 - 1694^2
------------------------
2

x= -(-18)± -1712
------------------------
2

i do not know how to deal with removing the /2 .

Answer 23

oops. "-18^2 - 1694^2" was meant to be "-18 - 1694"

Answer 24

and i am sure the -(-18^2) = 18^2 . though i have not changed it as i was working on the square root .

Answer 25

while editing the text for this reply ;)

Answer 26

fully corrected version:

x^2 -18x +77 =0

a=1 b=-18 c=77

x= -(-18)± √(-18^2 - 4*1*77)
------------------------
2


x= 18 ± √(-18^2 - 3388)
------------------------
2


x= 18 ± √(-18^2 - 1694^2)
------------------------
2

x= 18 ± -18 - 1694
------------------------
2

x= 18 ± -1712
------------------------
2

Answer 27

it is the ± that i am not sure of. i wold guess that i make two different problems and remove the /2 that way. o_O ?

Answer 28

it is time for me to go. i will check back tomorrow, thanks.

Answer 29

really sorry. didnt c ur reply. let me chck nw.