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Mathematics 13 Online
OpenStudy (brightemmerald):

What number must you add to complete the square? x^2 + 10x = 8 A. 25 B. 10 C. 5 D. 15

OpenStudy (johnweldon1993):

To complete the square: 1) Take the coefficient of the 'x' term --> 10 here 2) Divide it by 2 --> So (10/2) = 5 3) Square the result --> So 5^2 = 25 4) Add it to both sides of the equation Meaning your answer is...?

OpenStudy (brightemmerald):

25x^2+10x=32?

OpenStudy (brightemmerald):

so the answer is either a or c?

OpenStudy (brightemmerald):

*my mind is broken whilst doing math*

OpenStudy (johnweldon1993):

Not quite. Why did you combine the 25 and the x^2 term? So the goal here is to get our equation from \[\large x^2 + 10x = 8\] To something that looks like \[\large x^2 + 10x + \text{__} = c\] Which will ultimately factor into \[\large (x + \text{something})^2 = c\]

OpenStudy (brightemmerald):

Uhh

OpenStudy (johnweldon1993):

So here...from the beginning \[\large x^2 + 10x = 8\] We take the coefficient of the 'x term and divide it by 2...and the square the result --> (10/2)^2 = 25 Now we add that to both sides of the equation \[\large x^2 + 10x + 25 = 8 + 25\] \[\large x^2 + 10x + 25 = 32\]

OpenStudy (johnweldon1993):

So that is it...in order to complete the square...we just needed to add 25 to the equation

OpenStudy (brightemmerald):

Oh! Okay, so 25 is the perfect square, but 5 is the square itself.

OpenStudy (johnweldon1993):

Exactly!

OpenStudy (brightemmerald):

THANK YOU SO MUCH!

OpenStudy (johnweldon1993):

Not a problem!

OpenStudy (brightemmerald):

Im getting ready to post another question... lol I have so many!

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