Ray1998
  • Ray1998
What are the solutions of the quadratic equation? 2x^2 - 16x + 32 = 0 Will give fan and medal. Thank you in advance! :)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
The solution is x = 4
Ray1998
  • Ray1998
Okay. Um, thank you, but could you tell me how? Like walk through with me how you got that answer? @Cardinal_Carlo
anonymous
  • anonymous
Do you know the quadratic formula?

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Ray1998
  • Ray1998
No, sorry. @OrangeMaster
anonymous
  • anonymous
\[2(x ^{2} - 8x + 16) = 0\] \[(x-4)^{2} = 0\] \[x = 4\]
anonymous
  • anonymous
It is essential to answering the question. It is x= -b +/- sqrt(b^2-4ac)/2a
anonymous
  • anonymous
The quadratic formula is too complicated and therefore impractical to use it in this particular case. But it is similarly effective.
anonymous
  • anonymous
\[x=\frac{ -b \pm \sqrt{b^{2}-4ac} }{ 2a }\]
Ray1998
  • Ray1998
Okay. How do you apply that to the equation though?
Ray1998
  • Ray1998
It's not needed?
anonymous
  • anonymous
2x^2 - 16x + 32 = 0 The 2 in front of x is 'a' -16 is 'b' 32 is 'c' Input the values and solve.
anonymous
  • anonymous
\[x=\frac{ -(-16) \pm \sqrt{-16^{2}-4(2)(32)}}{ 2(2) }\]
ybarrap
  • ybarrap
Here's a fun way $$ (x - ?)^2+16 - ?^2=0\\ $$ To find that ? just take the coefficient of x, in this case 8 and divide it by 2 $$ (x - \cfrac{8}{2})^2+16 - \left (\cfrac{8}{2}\right )^2=0\\ $$ Just another approach.
anonymous
  • anonymous
-(-16)=16 -16^2=256 4*2*32=256 256-256=0 sqrt(0)=0 2*2=4 16/4=4
anonymous
  • anonymous
The plus/minus has no point when the sqrt of 4ac is 0
Ray1998
  • Ray1998
-3^2 + 16 - 4^2 = -9 ? @ybarrap
anonymous
  • anonymous
@ybarrap method works but it's confusing for starters
anonymous
  • anonymous
So, @Cardinal_Carlo is correct, but there's the explanation.
anonymous
  • anonymous
Or, an explanation rather.
Ray1998
  • Ray1998
Okay. Gotcha. Sorry guys, let me just read through what all of you said :) thank you very very much for helping me. I'm trying to understand. @OrangeMaster @Cardinal_Carlo @ybarrap
anonymous
  • anonymous
No problem, just try to use what is easiest for you to understand. :)
ybarrap
  • ybarrap
No x variables? $$ -3^2 + 16 - 4^2 = -9 $$ If so $$ -3^2 + 16 - 4^2 =-9+16-16=-9 $$ So the statement is true.
Ray1998
  • Ray1998
I think I'm starting to understand it a little. I see both of your methods and I feel a better about them :)
anonymous
  • anonymous
The quadratic formula may be hard to memorize and understand at first, but it will get the problem solved.
Ray1998
  • Ray1998
Okay. Thank you.
Ray1998
  • Ray1998
Thank you guys SO much! @OrangeMaster @Cardinal_Carlo @ybarrap
ybarrap
  • ybarrap
You're welcome $$ \color{green}{\Huge {:-)}} $$
anonymous
  • anonymous
You're welcome

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