find all real or imagined solutions for 49x^2 + 9 = 42x

[rn50nurse]

Okay- I think i am making it hard again-- find all real or imagined solutions
49x^2+9=42x

Here is what i did so far:
49x^2+9+42x=0
40x^2+42 x+9=0
Then I factor getting (7x-6)(7x-7)
7x-7=0 or
7x-6 = 0
x= -6/7 or x=-1

solution sets {-6/7, -1}
am I totally on the wrong track??? :?:

 

[pka]

\(\displaystyle \L 49x^2 + 9 = 42x\quad \Leftrightarrow \quad 49x^2 - 42x + 9 = 0\)

Now FACTOR.

 

[galactus]

\(\displaystyle \L\\49x^{2}-42x+9=0\)

To factor, what two numbers when added equal -42 and when multiplied equal 441(49*9=441)?.

How about -21 and -21.

\(\displaystyle \L\\49x^{2}-21x-21x+9=0\)

Now group and factor. Make sure you have the same thing inside the parentheses, otherwise, it won't work.

 

[stapel]

find all real or imagined solutions

No wonder you're confused! :shock:

Your book should have been referring to "imaginary" or "complex" solutions (that is, solutions involving imaginary or complex numbers), not "imagined" solutions (pretend "solutions", made up in somebody's head).

Note: To move the "42x" from the right-hand to the left-hand side of the equation, one would need to subtract it from either side, which would put a "minus" sign in front. In other words, this works just like back when you were solving linear equations.

Eliz.

 

[rn50nurse]

THANKS!!! I just couldn't seem to get my brain around it!!!