# How do you solve using the square root property 4x^2 – 8x – 2 = 0?

Refer to explanation

#### Explanation:

The Square Root Property

For any positive number k, if ${x}^{2} = k$ then $x = \sqrt{k}$ or $x = - \sqrt{k}$

We want to use the above property to solve the equation given hence we have that

$4 {x}^{2} - 8 x - 2 = 0 \implies 4 \cdot \left({x}^{2} - 2 x + 1\right) - 6 = 0 \implies {\left(x - 1\right)}^{2} = \frac{6}{4} \implies {\left(x - 1\right)}^{2} = \frac{3}{2}$

Hence ${\left(x - 1\right)}^{2} = \frac{3}{2}$ using the square root property we get

$\left(x - 1\right) = \sqrt{\frac{3}{2}} \implies x = 1 + \sqrt{\frac{3}{2}}$

or

$\left(x - 1\right) = - \sqrt{\frac{3}{2}} \implies x = 1 - \sqrt{\frac{3}{2}}$