Algebra hard

Today we learned x2+px+q=0

So for instance :

x2+7x-3,75=0 would be:

x = -3,5 + & - square root of 12,5+3,75
x = -3,5 + & - square root of 16,25
x = -3,5 + & - 4

x1 = ~ 0,5
x2 = ~ -7,5

Our teacher said that this would be the hardest part of our subject for this moment but I found this method to be the easiest out of them all

Just a question

So we know that for instance:

5x^2 - 50x = -80
5x^2 - 50x + 80 = 0
x^2 - 10x + 16 = 0
x = 5 + & - square root of 25-16
x = 5 + & - square root of 9
x = 5 + & - 3
x1 = 8
x2 = 2

But what about this equation:


2219) D) how to solve this?

This post was edited by xaz on Feb 22 2018 01:56pm

move 9 over and rearrange so you get -y^2+10y-9 = 0

multiply both sides by -1 and you get y^2-10y+9 = 0

quadratic formula is easiest here


a = 1
b= -10
c = 9

one y will be

y = (10 + sqrt(-10^2 - 4*9))/2

= (10 + sqrt(64))/2

= (10 + 8)/2

= 9

the other y will be

y = (10 - sqrt(-10^2 - 4*9))/2

= (10 - sqrt(64))/2

= (10 -8)/2

= 1

try substituting y for 9 and 1 in the equation y^2-10y+9=0 and you will see that both 9 and 1, when substituted for y, will give you 0

This post was edited by Zpot on Feb 23 2018 12:32am

Sorry my bad, meant to say C)
I had n problem solving a, b and d
It's C that I can't figure out

I'm assuming the commas are decimal places. I'd start by multiplying both sides by 2 to get

z^2-z+0.25=0

this one is really easy if you break it down like this (the quadratic formula essentially always works so I do that on funky looking ones but this one is actually surprisingly straightforward)

(z-0.5)(z-0.5) = 0

If you foil (front outside inside last) you will get z^2-z+0.25. There's only one possible answer for z and it's 0.5

z-0.5 = 0 add 0.5 to both sides and you get z = 0.5

If the teacher hasn't showed you foil, you multiply the front 2 terms (z*z) to get z^2, multiply the outside terms (z*-0.5) gives you -0.5z, multiply the inside terms (-0.5*z) gives you -0.5z, and multiply the last 2 terms (-0.5*-0.5) gives you 0.25. This gives you z^2, combine the like terms -0.5z and -0.5z to get -z, and -0.5*-0.5 is 0.25.

This post was edited by Zpot on Feb 23 2018 02:34am

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