BC QR Test 5 Question 39

[capnamerica]

Could someone please explain the math behind this? I'm unclear on how x is solved for below.

Thanks!

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[KyoPhan]

Try to set it so that it's ax^2 + bx + c = 0,

Then use the quadratic equation. It will give you two answers as shown with the comma.

 

[cacajuate]

I would venture to guess that on the actual DAT that it will be a much easier number to factor out. Doubt they will make you use the quadratic equation, takes forever.

 

[pulltheleverkronk]

LOL no way they'll make you do the quadratic equation on the real thing. If they did, that would be the last question I'd answer...

 

[capnamerica]

Thanks y'all!

 

[tommyngu]

I never use the quadratic equation. Completing the square works every time if you can't factor a simpler way.
The equation simplifies a bit to
x^2 - 8x = -8
Once in this format, you can complete the square: basically add (b/2)^2 to both sides of the equation to get
x^2 - 8x + 16 = 8
Now the left side easily factors to
(x - 4)^2 = 8
Take the square root of both sides
x - 4 = (+/-)2*sqroot(2)
Which simplifies to your answer.

Quick instructions to complete the square:
1. write the equation in the form ax^2 + bx = c
2. if a is anything other than 1, divide each term by a to remove the coefficient
3. add (b/2)^2 to both sides of the equation
4. factor the left side: (it will factor to (x + (b/2))^2)
5. take the square root of both sides and simplify to get your answer.

 

[cacajuate]

I never use the quadratic equation. Completing the square works every time if you can't factor a simpler way.
The equation simplifies a bit to
x^2 - 8x = -8
Once in this format, you can complete the square: basically add (b/2)^2 to both sides of the equation to get
x^2 - 8x + 16 = 8
Now the left side easily factors to
(x - 4)^2 = 8
Take the square root of both sides
x - 4 = (+/-)2*sqroot(2)
Which simplifies to your answer.

Quick instructions to complete the square:
1. write the equation in the form ax^2 + bx = c
2. if a is anything other than 1, divide each term by a to remove the coefficient
3. add (b/2)^2 to both sides of the equation
4. factor the left side: (it will factor to (x + (b/2))^2)
5. take the square root of both sides and simplify to get your answer.

This is why I am bad at the qr section, my math knowledge is weak. Good post Tommy

 

[capnamerica]

I never use the quadratic equation. Completing the square works every time if you can't factor a simpler way.
The equation simplifies a bit to
x^2 - 8x = -8
Once in this format, you can complete the square: basically add (b/2)^2 to both sides of the equation to get
x^2 - 8x + 16 = 8
Now the left side easily factors to
(x - 4)^2 = 8
Take the square root of both sides
x - 4 = (+/-)2*sqroot(2)
Which simplifies to your answer.

Quick instructions to complete the square:
1. write the equation in the form ax^2 + bx = c
2. if a is anything other than 1, divide each term by a to remove the coefficient
3. add (b/2)^2 to both sides of the equation
4. factor the left side: (it will factor to (x + (b/2))^2)
5. take the square root of both sides and simplify to get your answer.

Very helpful. Thanks!