How do you multiply x10−12=−35x?

1 Answer
Don't Memorise
May 9, 2015

Given:
x10−12=−35x

to make the denominator of the L.H.S equal we take the L.C.M:

L.C.M of 10 and 2 = 10

(x10)−1×52×5=−35x
(x10)−510=−35x

x−510=−35x
on cross multiplying:

(x−5)×(5x)=−3×10

5x2−25x=−30

5x2−25x+30=0

dividing the equation by 5:
x2−5x+6=0

solving this equation by grouping / splitting the middle term:

x2−2x−3x+6=0 (2×3=6and2+3=5)

=x(x−2)−3(x−2)

=(x−2)(x−3)

x has two values here:
x=2andx=3

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