Question

30 POINTS IF YOUR COMPLETE NUMBER 5

Answer 1

Explanation:

`4(g-1)^(2) +6=13`

First we expand the brackets:

`4(g-1)(g-1)+6=13`

`(4g-4)(g-1)+6=13`

`4g^(2) -4g-4g+4+6=13`

`4g^(2) -8g+10=13`

Now make it into a quadratic in the form
`ax^(2) +bx+c=0`:

`4g^(2) -8g -3=0`

Now using the quadratic formula:

`x=\frac{-b(+/-)\sqrt{b^(2)-4ac} }{2a}`
We can solve for g:

`g_(1)` =
`(2+√(7) )/(2)`

`g_(2)` =
`(2-√(7) )/(2)`

Answer 2

`g=(√(7))/(2)+1` or
`g=-(√(7))/(2)+1`

Explanation:

`4\left(g-1\right)^2+6=13`

`4\left(g-1\right)^2=13-6`

`4\left(g-1\right)^2=7`

`\left(g-1\right)^2=(7)/(4)`

`g-1 = \pm\sqrt{(7)/(4) }`

`g =\pm \sqrt{(7)/(4) }+1`

Final answer:

`g=(√(7))/(2)+1` or
`g=-(√(7))/(2)+1`