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Question

Solve the following equation:
x+1+4x+13=3x+12

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Solution

x+1+4x+13=3x+12
squaring both sides
x+1+4x+13+2x+14x+13=3x+12
2x+13x+13=3x+125x14=2x2
2x+14x+13=2(x+1)
squaring both sides
(x+1)(4x+13)=(x+1)2=x2+1+2x
4x2+4x+13+13x=x2+2x+1
3x2+15x+12=0
x2+5x+4=0
x2+4x+x+4=0
x(x+4)+(x+4)=0
(x+4)+(x+4)=0
x=1,4
Hence, the answer is 1,4.


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