solving quadratic equations using form ax^2= k

[musicrocks429]

how to solve quadratic equations of the form of ax^2=k how do you work these out? my teacher didn't explain to us.
example1. 2x^2+18=40

example 2. 2x^2-162=0

example3. x^2-11=70

 

[jwpaine]

I'll help you on the first one.

For starters..You want to start with your equation equaling 0. It's not necessary, but makes good practice for when you get into solving larger polynomials.

2x^2+(18-40) = 0
2x^2-22 = 0

now divide everything by 2, to get x^2 by itself.

(2x^2 - 22 )/2 = 0
x^2 -(22/2) = 0

which gives us
x^2 - 11 = 0

now move the 11 to the other side so we can solve for x
x^2 = 11

squareroot both sides, to get x by it's self.
squareroot(x^2) = squareroot(11)

x = + or - the squareroot(11)


Your teacher should have gone over this before giving homework. :roll:

Do the same on all the rest.

 

[musicrocks429]

thanks a lot. i was seriously lost on this.

 

[Denis]

how to solve quadratic equations of the form of ax^2=k how do you work these out? my teacher didn't explain to us.
example1. 2x^2+18=40

This way is faster; isolate the x term:
2x^2 = 22
x^2 = 11
x = +-sqrt(11)