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Question

Solve the following equations:
2x29x+4+32x1=2x2+21x11.

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Solution

2x29x+4+32x1=2x2+21x112x29x+4+32x12x2+21x11=02x28xx+4+32x12x2x+22x11=02x(x4)1(x4)+32x1x(2x1)+11(2x1)=0(2x1)(x4)+32x1(x+11)(2x1)=02x1(x4+3x+11))=0
2x1=0 x=12
and x4+3x+11=0
x4+3x+11=0x4+3=x+11
Squaring both sides
x4+9+6x+4=x+116x4=6x4=1
Again squaring both sides
x4=1x=5
So the values of x are 12 and 5

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