# How do you solve 4x^2-7x+1=0 using the quadratic formula?

x=~1.6,~0.16

#### Explanation:

From the equation in standard form ($a {x}^{2} + b x + c = 0$), take the a, b, and c terms and sub them into the quadratic formula:

$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

$x = \frac{- \left(- 7\right) \pm \sqrt{{7}^{2} - 4 \left(4\right) \left(1\right)}}{2 \cdot 4}$

$x = \frac{7 \pm \sqrt{33}}{8}$

Now solve for the positive and negative roots.

Positive:

$x = \frac{7 + \sqrt{33}}{8}$
x=~1.6

Negative:

$x = \frac{7 - \sqrt{33}}{8}$
x=~0.16