First factor 2 from the quadratic:
[tex]2x^2+12x-14=2(x^2+6x-7)[/tex]
Now complete the square:
[tex]x^2+6x-7=x^2+6x+9-16=(x+3)^2-16[/tex]
So we have
[tex]2x^2+12x-14=0\implies2(x+3)^2-32=0[/tex]
[tex]\implies2(x+3)^2=32[/tex]
Solve for x:
[tex](x+3)^2=\dfrac{32}2=16[/tex]
[tex]x+3=\pm\sqrt{16}=\pm4[/tex]
[tex]\implies x=-3+4=1\text{ OR }x=-3-4=-7[/tex]
and so the third option is correct.
