Question

2x^2+12x-14=0 by completing the square

Answer 1

First factor 2 from the quadratic:

`2x^2+12x-14=2(x^2+6x-7)`

Now complete the square:

`x^2+6x-7=x^2+6x+9-16=(x+3)^2-16`

So we have

`2x^2+12x-14=0\implies2(x+3)^2-32=0`

`\implies2(x+3)^2=32`

Solve for x:

`(x+3)^2=\frac{32}2=16`

`x+3=\pm√(16)=\pm4`

`\implies x=-3+4=1\text{ OR }x=-3-4=-7`

and so the third option is correct.