Question

30 POINTS IF YOUR COMPLETE NUMBER 5

Answer 1

Answer:

$g=\frac{\sqrt{7}}{2}+1$ or $g=-\frac{\sqrt{7}}{2}+1$

Step-by-step explanation:

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

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

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

$\left(g-1\right)^2=\frac{7}{4}$

$g-1 = \pm\sqrt{\frac{7}{4} }$

$g =\pm \sqrt{\frac{7}{4} }+1$

Final answer:

$g=\frac{\sqrt{7}}{2}+1$  or  $g=-\frac{\sqrt{7}}{2}+1$

Answer 2

Answer:

Step-by-step 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:

$g_{1}$ = $\frac{2+\sqrt{7} }{2}$        
$g_{2}$  = $\frac{2-\sqrt{7} }{2}$