SOLUTION: Factor the following: -20+31x-12x^2

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Question 535922: Factor the following: -20+31x-12x^2
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Write the opposite way
+-12x%5E2+%2B+31x+-+20+
Use the quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+a+=+-12+
+b+=+31+
+c+=+-20+
x+=+%28+-31+%2B-+sqrt%28+31%5E2+-+4%2A%28-12%29%2A%28-20%29+%29%29%2F%282%2A%28-12%29%29+
x+=+%28+-31+%2B-+sqrt%28+961+-+960+%29%29%2F-24+
x+=+%28+-31+%2B-+sqrt%28+1+%29%29%2F-24+
x+=+%28+-31+%2B+1+%29+%2F+-24+
x+=+-30%2F-24+
+x+=+5%2F4+
and
x+=+%28+-31+-+1+%29+%2F+-24+
+x+=+-32%2F-24+
+x+=+4%2F3+
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I can also say
+-x+=+-%285%2F4%29+
(1) +-x+%2B+5%2F4+=+0+
multiply both sides by 4
(1) +-4x+%2B+5+=+0+
and
+x+=+4%2F3+
(2) +x+-+4%2F3+=+0+
multiply both sides by 3
(2) +3x+-+4+=+0+
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Multiply (1) and (2)
+%28-4x+%2B+5%29%2A%283x+-+4%29+=+0+
+-12x%5E2+%2B+31x+-+20+=+0
So, the factors are
+-4x+%2B+5+
and
+3x+-+4+