Solve Using the Quadratic Formula 7x^2+100x-4=0

$7 x^{2} + 100 x - 4 = 0$

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 $a = 7$ , $b = 100$ , and $c = - 4$ into the quadratic formula and solve for $x$ .

$\frac{- 100 \pm \sqrt{100^{2} - 4 \cdot (7 \cdot - 4)}}{2 \cdot 7}$

Step 3

Simplify.

Simplify the numerator.

Raise $100$ to the power of $2$ .

$x = \frac{- 100 \pm \sqrt{10000 - 4 \cdot 7 \cdot - 4}}{2 \cdot 7}$

Multiply $- 4 \cdot 7 \cdot - 4$ .

Multiply $- 4$ by $7$ .

$x = \frac{- 100 \pm \sqrt{10000 - 28 \cdot - 4}}{2 \cdot 7}$

Multiply $- 28$ by $- 4$ .

$x = \frac{- 100 \pm \sqrt{10000 + 112}}{2 \cdot 7}$

Add $10000$ and $112$ .

$x = \frac{- 100 \pm \sqrt{10112}}{2 \cdot 7}$

Rewrite $10112$ as $8^{2} \cdot 158$ .

Factor $64$ out of $10112$ .

$x = \frac{- 100 \pm \sqrt{64 (158)}}{2 \cdot 7}$

Rewrite $64$ as $8^{2}$ .

$x = \frac{- 100 \pm \sqrt{8^{2} \cdot 158}}{2 \cdot 7}$

Pull terms out from under the radical.

$x = \frac{- 100 \pm 8 \sqrt{158}}{2 \cdot 7}$

Multiply $2$ by $7$ .

$x = \frac{- 100 \pm 8 \sqrt{158}}{14}$

Simplify $\frac{- 100 \pm 8 \sqrt{158}}{14}$ .

$x = \frac{- 50 \pm 4 \sqrt{158}}{7}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{- 50 \pm 4 \sqrt{158}}{7}$

Decimal Form:

$x = 0.03988862 \dots, - 14.32560290 \dots$