What are the solutions to the quadratic equation 5x2 + 60x = 0?
x = 0 and x = −12
x = 0 and x = 12
x = 5 and x = −12
x = 5 and x = 12

- anonymous

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- taramgrant0543664

Do you have an idea on how to do this?

- anonymous

I think I do somewhat

- UsukiDoll

factor out the like terms for
\[5x^2+60x=0\]

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## More answers

- anonymous

Aren't I supposed to find what 5^2 and 60 have in common or something like that or I am mistaken ._.

- UsukiDoll

yeah.... you are supposed to find what they have in common and yank em out.

- taramgrant0543664

Well in order to get 0 on the right we know that x=0 in one case because substituting 0 in we will get 0 on the left

- taramgrant0543664

To find the second number you have to factor out what you can so what can you factor out?

- UsukiDoll

let's split this up for a sec
\[5x^2+(5)(12)x=0\]
ok what number do they have in common and what variable do they have in common?

- anonymous

They have 5 and 12 in common.... 5 and 12 have..... 3 in common I guess.... since 3 times 3 is 12 and 3 +2 = 5

- taramgrant0543664

They both have 5x in common so you can factor that out

- taramgrant0543664

So 5x(x+12)=0

- UsukiDoll

how is 3 x 3 12?
3 x 3 = 9

- anonymous

I meant 3 times 4 sorry

- taramgrant0543664

To get the inside the brackets equal to 0 how do you get that?

- UsukiDoll

well 12 x 5 = 60. when I split it up we have a 5 for the number in common and x for the variable in common so 5x gets yanked out
and we're left with
5x(x+12)=0
now we solve for x for these two cases
5x = 0 and x +12 = 0

- anonymous

By subtracting because we want less?

- pooja195

Solve both for x

- anonymous

x = 0 its so simple ._.

- UsukiDoll

@pooja195 yes solve both equations for x

- pooja195

5x = 0 (divide)
x +12 = 0 (sibtract)

- taramgrant0543664

(X+12)=0 you want some number to be negative so it equals 0

- UsukiDoll

we want x by itself for x+12=0
so we subtract both sides by 12

- anonymous

The answer is still zero since 0 minus 12 is 12 and 12 divided by 0 is ZERO so both answers are Zero :D

- UsukiDoll

omg I am facepalming over this.

- UsukiDoll

there are two solutions of x.

- UsukiDoll

we got x = 0 for 5x=0
now solve
x+12 = 0
by subtracting 12 on both sides.

- anonymous

Its 11pm I have had a long day I am already bad at math add me doing this half asleep.....

- anonymous

I DID!

- pooja195

0-12?

- taramgrant0543664

X+12=0
x+12-12=0-12

- anonymous

GOD ITS LIKE 6th grade ALGEBRA! 12 minus zero is 12

- taramgrant0543664

Zero minus twelve not twelve minus zero

- anonymous

Well Negative 12

- UsukiDoll

thank you @taramgrant0543664

- anonymous

But it is still 12

- anonymous

Just on the left side XD

- taramgrant0543664

Zero minus twelve is negative twelve

- anonymous

I just said that ._.

- UsukiDoll

5x(x+12) = 0
5x = 0
divide 5 on both sides and we have x = 0
x+12 = 0
-12 -12
x = -12

- taramgrant0543664

It's not twelve it's negative twelve

- anonymous

Well sorry! The answer is A i finally finished the test thanks and sorry for being a freaking idiot..... its just late and I have been doing work all day and by now my head is just on fire ._. I am going to bed good night

- anonymous

@UsukiDoll
Sarcasm is one of my many flaws its an aspect of my personality I have to fix...... I am very sorry if I was a jerk or I offended you in any way thanks for the help and patients both you and @taramgrant0543664

- UsukiDoll

ah... that's ok. I take meds in real life or get high blood pressure so I type some crazy stuff sometimes too. XD

- mathstudent55

\(\Large 5x^2 + 60x=0\)
Factor out the common factor 5x:
\(\Large \color{red}{5x} \cdot x + 12 \cdot \color{red}{5x} = 0\)
\(\Large 5x(x + 12) = 0\)
Divide both sides by 5:
\(\Large x(x + 12) = 0\)
Set both factors equal to 0:
\(\Large x = 0\) or \(\Large x + 12 = 0\)
Solve both equations for x:
\(\Large x = 0\) or \(\Large x = -12\)

- anonymous

lol ok

- UsukiDoll

meow ^.^

- anonymous

Oh and I got an 89% in the test! XD

- anonymous

So double thanks now good night and bye

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