Solve Using the Quadratic Formula 5x^2-28x+19=0

$5 x^{2} - 28 x + 19 = 0$

Step 1

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 2

Substitute the values $a = 5$ , $b = - 28$ , and $c = 19$ into the quadratic formula and solve for $x$ .

$\frac{28 \pm \sqrt{{(- 28)}^{2} - 4 \cdot (5 \cdot 19)}}{2 \cdot 5}$

Step 3

Simplify.

Simplify the numerator.

Raise $- 28$ to the power of $2$ .

$x = \frac{28 \pm \sqrt{784 - 4 \cdot 5 \cdot 19}}{2 \cdot 5}$

Multiply $- 4 \cdot 5 \cdot 19$ .

Multiply $- 4$ by $5$ .

$x = \frac{28 \pm \sqrt{784 - 20 \cdot 19}}{2 \cdot 5}$

Multiply $- 20$ by $19$ .

$x = \frac{28 \pm \sqrt{784 - 380}}{2 \cdot 5}$

Subtract $380$ from $784$ .

$x = \frac{28 \pm \sqrt{404}}{2 \cdot 5}$

Rewrite $404$ as $2^{2} \cdot 101$ .

Factor $4$ out of $404$ .

$x = \frac{28 \pm \sqrt{4 (101)}}{2 \cdot 5}$

Rewrite $4$ as $2^{2}$ .

$x = \frac{28 \pm \sqrt{2^{2} \cdot 101}}{2 \cdot 5}$

Pull terms out from under the radical.

$x = \frac{28 \pm 2 \sqrt{101}}{2 \cdot 5}$

Multiply $2$ by $5$ .

$x = \frac{28 \pm 2 \sqrt{101}}{10}$

Simplify $\frac{28 \pm 2 \sqrt{101}}{10}$ .

$x = \frac{14 \pm \sqrt{101}}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{14 \pm \sqrt{101}}{5}$

Decimal Form:

$x = 4.80997512 \dots, 0.79002487 \dots$