Question

Someone please help:

Solve x^2 - 3x = -8.

Answer 1

first of all we will calculate the discriminant "d" of x^2-3x+8=0
d=(-3)^2-4*8*1=9-32=-23<0 so the equation has no solution in IR
do you want the complex solutions ??

Answer 2

How did you get those numbers?

Answer 3

Oh nevermind.

Answer 4

It says to solve using the quadratic formula.

Answer 5

okay so I'm going to do it step by step

Answer 6

I'm gonna start with the general case ax^2+bx+c=0
in our case a=1, b=-3 and c=8
the steps so that you can get the quadratic formula are:
step 1:
x^2 + \frac{b}{a} x= -\frac{c}{a}.

Answer 7

I'm sorry the last expression is:
x^2+b/a*x=-c/a so here we move c to the other side and we devide by a

Answer 8

step 2
we add to our expression ((1/2)*(b/a))^2 to both sides of the equality
x^2+b/a*x+((1/2)*(b/a))^2=-c/a+((1/2)*(b/a))^2

Answer 9

on the first hand we have:
x^2+b/a*x+((1/2)*(b/a))^2=(x+b/(2a))^2 (you can check it)

Answer 10

and now all we have to do is to replace by the values of a, b and c in
(x+b/(2a))^2=-c/a+((1/2)*(b/a))^2
a=1, b=-3 and c=8
(x-3/2)^2=(-16+9)/2)=-7/2
as you can observe (x-3/2)^2 is positive and it can't equal something negative
conclusion: the equation has no solutions.

Answer 11

The problem is asking for a specific answer using imaginary numbers: i

Answer 12

So far I have: x = 3 +/- (sqrt)[-17] / 2

Answer 13

okay you want complex solutions

Answer 14

The answer includes imaginary number i

Answer 15

so let's start from the last thing I wrote
(x-3/2)^2=(-16+9)/2)=-7/2

Answer 16

we can write (-7/2) = (i*sqrt(7/2))^2 right !

Answer 17

Is that the simplified form?

Answer 18

no not yet actually I made a mistake in calcula it's -7/4
so (-7/4)=(i*sqrt(7)/2)^2
we replace (x-3/2)^2=(i*sqrt(7)/2)^2

Answer 19

Okay what's the next step?

Answer 20

we pass to the sqrt of the expression and we get
abs(x-3/2)=i*sqrt(7)/2

Answer 21

Is that it?

Answer 22

is it clear until now ?

Answer 23

Mostly.

Answer 24

What's next?

Answer 25

First move -8 to left hand side , for that you have to add 8 on both sides , then you will get quadratic equation . So use quadratic formula and solve for x ,.... Hope this will help you

Answer 26

abs(x-3/2)=i*sqrt(7)/2
so we have two cases (|a|=b -->a=b or a=-b)
so x-3/2=i*sqrt(7)/2 or x-3/2=-i*sqrt(7)/2
i.e. x=3/2+i*sqrt(7)/2 or x=3/2-i*sqrt(7)/2 those are the solutions

Answer 27

Neither of those fit the answer choices.

Answer 28

both of them are correct we don't have one solution but we have a set of solutions
{3/2+i*sqrt(7)/2,3/2-i*sqrt(7)/2}
but I recommand you to do again the calcul if there is any mistake

Answer 29

all of the choices are either to the sqrt of 29 or 23