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Solve quadratic equation by completing the square. Check both roots.
problem below
 one year ago
 one year ago
Solve quadratic equation by completing the square. Check both roots. problem below
 one year ago
 one year ago

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countonme123Best ResponseYou've already chosen the best response.1
\[2x^212x +16=0\]
 one year ago

countonme123Best ResponseYou've already chosen the best response.1
please explain each step I am having trouble with it
 one year ago

SonitaBest ResponseYou've already chosen the best response.0
2(x^26x+8)=0 2[(x4)(x2)]=0
 one year ago

countonme123Best ResponseYou've already chosen the best response.1
please do explain why you do each step
 one year ago

NotTimBest ResponseYou've already chosen the best response.0
1st step Factor out 2. Second step What 2 numbers add to the end value, and multiply to the middle value?
 one year ago

NotTimBest ResponseYou've already chosen the best response.0
Those 2 values are then put into the brackets as you see them.
 one year ago

NotTimBest ResponseYou've already chosen the best response.0
And here, the signs of positive and negatives are reversed because when you solve for x individually, x4=0 x=4. Ok?
 one year ago

countonme123Best ResponseYou've already chosen the best response.1
ok but there is supposed to be two answers
 one year ago

NotTimBest ResponseYou've already chosen the best response.0
eh, you might be might be making this more difficult than it actually is
 one year ago

peteweBest ResponseYou've already chosen the best response.1
I did what the question asked. Solve quadratic equation by completing the square.
 one year ago

KingGeorgeBest ResponseYou've already chosen the best response.1
You made a small mistake. The 8 should also be multiplied by 2.
 one year ago

KingGeorgeBest ResponseYou've already chosen the best response.1
Leaving you with\[2(x^26x+99+8)=2((x3)^21)=2(x3)^22\]
 one year ago

KingGeorgeBest ResponseYou've already chosen the best response.1
Set equal to 0, and get \[2(x3)^22=0\implies(x3)^2=1\]Take the root, and solve. \[x3=\pm1\implies x=4\quad\text{or}\quad x=2\]
 one year ago

countonme123Best ResponseYou've already chosen the best response.1
ok george you are right now can you explain each step
 one year ago

KingGeorgeBest ResponseYou've already chosen the best response.1
The hardest part is the first couple steps. You start with \[2x^212x+16=2(x^26x+8)\]The next part is where you complete the square. You take half of \(6\), square it, and then add/subtract it. So you get\[2(x^26x+8)=2(x^26x+\left(\frac{6}{2}\right)^2\left(\frac{6}{2}\right)^2+8=2(x^26x+99+8)\]
 one year ago

KingGeorgeBest ResponseYou've already chosen the best response.1
Now you simplify as I described before. It's important that you simplify \[x^26x+99+8\]as \((x3)^21\). That's the whole point of completing the square. You add/subtract just the right amount so you can have the square of a binomial. From there, you can solve for that square easily, and then just take a square root.
 one year ago

KingGeorgeBest ResponseYou've already chosen the best response.1
Did this make sense?
 one year ago

countonme123Best ResponseYou've already chosen the best response.1
yes thank you but please view my next question
 one year ago
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