How do you factorise x (sqaured) -7x+12 ?

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Asked 2/22/2009 2:40:17 PM

Updated 6/20/2014 1:24:25 PM

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Flagged by jerry06 [6/20/2014 1:24:25 PM]

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User: How do you factorise x (sqaured) -7x+12 ?

Weegy: there are three main methods from which you can solve Method 1: Quadratic Formula The standard form of a quadratic equation is ax^2+bx+c=0 You have (1)x^2+(7)x+(10)=0 a=1, b=7, [ c=10 The solutions for x are: x=[-b+/-sqrt(b^2-4ac)]/2a x=[-7+/-sqrt(49-4*1*10)]/2 x=[-7+/-sqrt(49-40)]/2 x=[-7+/-sqrt9]/2 x=[-7+/-3]/2 that's two solutions: x=[-7+3]/2 x=-4/2 x=-2 and x=(-7-3)/2 x=-10/2 x=-5 thus the solutions are -2 and -5 Method 2: Factoring to factor the quadratic: ax^2+bx+c=0 think of two such numbers that add to b and have a product equal to the product of a and c in your case, x^2+7x+10=0 think of 2 such numbers that add to 7 and have a product of 10 look at all the factors of 10 1x10 2x5 1+10=11, so this is not it 2+5=7, this is it Now rewrite x^2+2x+5x+10=0 look at the two parts separately x^2+2x the GCF is x it is factored to: x(x+2) and 5x+10 has a GCF of 5 so is factored to: 5(x+2) combine again x(x+2)+5(x+2)=0 because they have the same term (x+2), they are like terms that can be further factored (x+5)(x+2)=0 if the product of two numbers is 0, one of them must be 0 thus, the two solutions are: x+5=0, x=-5 and x+2=0, x=-2 that's -2 and -5 Method 3: Complete the Square this is my favorite. i think this might be the easiest x^2+7x+10=0 remove the constant from the left to the right by subtracting 10 x^2+7x=-10 a complete square is: (a+b)^2=a^2+2ab+b^2 so far we have: (x)^2+2(x)(7/2)=-10 that's a^2+2ab to complete, add b^2, or (7/2)^2 x^2+2*x*7/2+(7/2)^2=49/4-10 because (7/2)^2=7^2/2^2 thus, (x+7/2)^2 which is (a+b)^2 =(x)^2+2(x)(7/2)+(7/2)^2 which is a^2+2ab+b^2 furthermore, (x+7/2)^2=49/4-10 49/4-10 =49/4-40/4 =(49-40)/4 =9/4 (x+7/2)^2=9/4 x+7/2=+/-sqrt(9/4) sqrt(9/4)=sqrt9/sqrt4 thats 3/4 x=-7/2+/-3/2 thats the two solutions: x=-7/2-3/2=-10/2=-5 x=-7/2+3/2=-4/2=-2 and that's -2 and -5 ]
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Question

Asked 2/22/2009 2:40:17 PM

Updated 6/20/2014 1:24:25 PM

1 Answer/Comment

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Flagged by jerry06 [6/20/2014 1:24:25 PM]

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jerry06

x^2 - 7x + 12 = (x - 4)(x - 3)

Added 6/20/2014 1:24:24 PM

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