Question

Can someone please help me?(Fill in the blanks) This is on Khan Academy too, I need it ASAP! if you answer right I'll mark you BRAINLIEST. ​

Answer 1

First divide both sides by 2:

$2x^2+7x+6=0\implies x^2+\dfrac72x+3=0$

Move the constant term to the right side:

$x^2+\dfrac72x=-3$

Since

$(x+y)^2=x^2+2xy+y^2$

we want to have

$2y=\dfrac72\implies y=\dfrac74$

Then

$\left(x+\dfrac74\right)^2=x^2+\dfrac72x+\dfrac{49}{16}$

So in our equation, we need to add 49/16 to both sides in order to complete the square:

$x^2+\dfrac72x+\dfrac{49}{16}=-3+\dfrac{49}{16}$

$\implies\left(x+\dfrac74\right)^2=\dfrac1{16}$