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Question

Solve for x. 12a+b+2x=12a+1b+12x


Solution

12a+b+2x=12a+1b+12x
12a+b+2x12x=12a+1b
2x2ab2x(2a+b+2x)2x=2a+b2ab
(2a+b)(2a+b+2x)2x=2a+b2ab
1(2a+b+2x)2x=12ab
ab=x(2a+b+2x)
ab+x(2a+b)+2x2=0
2x2+x(2a+b)+ab=0
x=(2a+b)±(2a+b)24×2×ab4
x=(2a+b)±(2a+b)28ab4
x=(2a+b)±4a2+4ab+b28ab4
x=(2a+b)±4a24ab+b24
x=(2a+b)±(2ab)24
x=(2a+b)±(2ab)4
x=2ab+2ab4 or x=2ab2a+b4
x=2b4 or x=4a4
 x=b2,a

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