Find the value of a

Question

A straight line with the equation:

$$y = 2x - 2$$

Passes through the x-intercept: $$\frac{4a^2+1}{4}$$

Find the value of a.

My process:

Since the straight line passes through the line:

$$ 2x - 2 = \frac{4a^2+1}{4}$$ $$ 8x - 8 = {4a^2+1}$$ $$ 8x - 9 = {4a^2}$$ $$ \frac{8x -9}{4} = {a^2}$$ Squareroot the following. Dont know how to squareroot in this site. $$ \frac{8x -9}{4} = {a}$$

The answer shoud be in numbers as far as I am concerned so I dont think my process is right. Please help. Thank-you

Answer 1

All $x$ intercepts occur when $y=0$.

Thus:

$$0=2x-2$$

$$x=1$$

Setting the second equation equal to one:

$$1=\frac{4a^2+1}{4}$$

$$4a^2=3$$

$$a=\pm\frac{\sqrt3}{2}$$