anonymous
  • anonymous
Solve the equation by factoring: x2 - 7x + 12 = 0 A) x = 3 or 4 B) x = -3 or 4 C) x = 3 or -4 D) x = -3 or -4
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
please don't just give me the answer.... I want to actually try to learn how to do it. Also, know how to do this the "plug and play" method, but I need to know how to do it when it's not multiple choice. Thanks!
jiteshmeghwal9
  • jiteshmeghwal9
sorry dude
anonymous
  • anonymous
why?

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More answers

jiteshmeghwal9
  • jiteshmeghwal9
first factorize the L.H.S. & then gt ur answer
anonymous
  • anonymous
LHS?
ParthKohli
  • ParthKohli
Hi, Sunshine! Would you like to know the whole process from the start?
anonymous
  • anonymous
yes please! Thanks Spiderman! haha
anonymous
  • anonymous
Sum = -7 Product = 12 two numbers -4 and -3 x^2 -4x - 3x + 12 =0 x(x-4) -3(x-4) (x-4) (x-3) x = 3 or x = 4
ParthKohli
  • ParthKohli
All right then. Do you know what the standard form of a quadratic equation is?
anonymous
  • anonymous
@Sunshine447 Did u understand!
anonymous
  • anonymous
@ParthKohli yes
ParthKohli
  • ParthKohli
Okay, what is it?
anonymous
  • anonymous
ax + bx + c = 0 right?
ParthKohli
  • ParthKohli
\(ax^2 + bx + c = 0\)* What you first do is find the product of \(a\) and \(c\). What are \(a\) and \(c\) here?
anonymous
  • anonymous
@Sunshine447 Did u understand my method????
anonymous
  • anonymous
a=1 and c=12
ParthKohli
  • ParthKohli
Right! What's the product of 1, 12?
anonymous
  • anonymous
12
ParthKohli
  • ParthKohli
Correct! :) Now you have to find two numbers that add to get \(b\) and multiply to get the product of \(a\) and \(c\).
ParthKohli
  • ParthKohli
Do you know two numbers such that: Their sum is -7. Their product is 12. ?
anonymous
  • anonymous
no
ParthKohli
  • ParthKohli
Hmm, you may find them by trial and error. Note that a negative number times a negative number is a positive number, so those numbers must be negative if the sum of negative.
anonymous
  • anonymous
-3 and -4
ParthKohli
  • ParthKohli
You got it! Now, we will 'split' the middle term with these coefficients. \(-7x = -3x - 4x \Longrightarrow x^2 - 7x + 12 = x^2 - 3x - 4x + 12\)
ParthKohli
  • ParthKohli
Do you get it till this point?
anonymous
  • anonymous
yeah i think so
ParthKohli
  • ParthKohli
Okay, now we basically factor by 'grouping'. What you must do is factor the first two and last two terms. \(x^2 - 3x = x(x - 3)\) \(-4x + 12 = -4(x - 3)\) Get it till here?
anonymous
  • anonymous
yeah
ParthKohli
  • ParthKohli
So, \(x^2 - 3x - 4x + 12 = x(x - 3) - 4(x - 3)\). \(x(x - 3) - 4(x - 3) \Longrightarrow ( x - 4)( x - 3)\)
ParthKohli
  • ParthKohli
Are you there? Do you get it?
anonymous
  • anonymous
yeah
ParthKohli
  • ParthKohli
Okay, so \((x - 4)(x - 3) = 0\). Do you know the 'zero-product rule'?
anonymous
  • anonymous
i dont think so
ParthKohli
  • ParthKohli
All right, you have two solutions here. \( \color{Black}{\Rightarrow x - 4 = 0}\) \( \color{Black}{\Rightarrow x - 3 = 0}\)
anonymous
  • anonymous
okay...
ParthKohli
  • ParthKohli
Can you solve those equations? That is how you get the solutions.
anonymous
  • anonymous
x=4 and 3
anonymous
  • anonymous
Thanks!
ParthKohli
  • ParthKohli
You're welcome!
TheViper
  • TheViper
\[\LARGE{x^2-7x+12=0}\]\[\Large{x^2-3x-4x+12=0}\]\[\Large{x(x-3)-4(x-3)=0}\]\[\Large{(x-3)(x-4)}\]\[\Large{\color{green}{x=3\space or \space4}}\]
TheViper
  • TheViper
So A. is the right answer ;)
TheViper
  • TheViper
Understood ???

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