First, divide by 7 so you have nothing in front.
[tex] x^{2} -7=0[/tex]
Then we proceed with completing the square:
Normally we would move the constant to the right but in this case, there is none.
Take half of the x coefficient and square it. Add it to both sides.
So that's -3.
Half is [tex]- \frac{3}{2} [/tex].
Square it:
[tex]( \frac{3}{2}) ^{2}= \frac{9}{4} [/tex]
Add it to both sides:
[tex] x^{2} -3x + \frac{9}{4} = 0 + \frac{9}{4} \\ x^{2} -3x+ \frac{9}{4}= \frac{9}{4}[/tex]
Write the perfect square on the left:
[tex](x- \frac{3}{2} ) ^{2} = \frac{9}{4} [/tex]
Square root both sides:
[tex]x- \frac{3}{2} = +/-\sqrt{ \frac{9}{4} } [/tex]
Solve for x:
[tex]x= \frac{3}{2} +/- \sqrt{ \frac{9}{4} } [/tex]
Which simplifies to:
[tex] x_{1} = 0 \\ x_{2} = 3[/tex]
Hope that helps.
