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Question

Solve the given quadratic equation by completing the square, 2x2+5x3=0

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Solution

The given quadratic equation is 2x2+5x3=0. Multiply the equation by 2 then we get 4x2+10x6=0.
Add and subtract 254 in the equation 4x2+10x6=0 to make a perfect square as shown below:

2x2+5x3=02x2+5x+2542543=0(2x)2+(2×2x×52)+(52)2+(2543)=0(2x+52)2494=0((a+b)2=a2+b2+2ab)(2x+52)2=4942x+52=±4942x+52=±722x+52=72,2x+52=722x=7252,2x=72522x=122,2x=222x=6,2x=1x=62,x=12x=3,x=12
Hence, x=12 or x=3.

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