Solve Using the Quadratic Formula h^2+28h-3=0

$h^{2} + 28 h - 3 = 0$

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 $a = 1$ , $b = 28$ , and $c = - 3$ into the quadratic formula and solve for $h$ .

$\frac{- 28 \pm \sqrt{28^{2} - 4 \cdot (1 \cdot - 3)}}{2 \cdot 1}$

Step 3

Simplify.

Simplify the numerator.

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

$h = \frac{- 28 \pm \sqrt{784 - 4 \cdot 1 \cdot - 3}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot - 3$ .

Multiply $- 4$ by $1$ .

$h = \frac{- 28 \pm \sqrt{784 - 4 \cdot - 3}}{2 \cdot 1}$

Multiply $- 4$ by $- 3$ .

$h = \frac{- 28 \pm \sqrt{784 + 12}}{2 \cdot 1}$

Add $784$ and $12$ .

$h = \frac{- 28 \pm \sqrt{796}}{2 \cdot 1}$

Rewrite $796$ as $2^{2} \cdot 199$ .

Factor $4$ out of $796$ .

$h = \frac{- 28 \pm \sqrt{4 (199)}}{2 \cdot 1}$

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

$h = \frac{- 28 \pm \sqrt{2^{2} \cdot 199}}{2 \cdot 1}$

Pull terms out from under the radical.

$h = \frac{- 28 \pm 2 \sqrt{199}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$h = \frac{- 28 \pm 2 \sqrt{199}}{2}$

Simplify $\frac{- 28 \pm 2 \sqrt{199}}{2}$ .

$h = - 14 \pm \sqrt{199}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$h = - 14 \pm \sqrt{199}$

Decimal Form:

$h = 0.10673597 \dots, - 28.10673597 \dots$